Installing windows on a MacBook Pro 15-Inch "Core 2 Duo" without Mac OS X
One technical reason you can not use rEFInd is that rEFInd is a boot manager. To boot Windows you need a boot loader. The rEFInd boot manager instructs the firmware which file or data to boot from. The actual booting is not done by rEFInd.
Grub is a boot loader. Grub may be able to boot Windows. However, Windows on your model Mac needs to interact with a functioning BIOS. No BIOS means no successful booting of Windows.
Installing 64 Bit BIOS Booting Windows 10

This installation method does not require OS X (macOS) to be installed on the Mac. However, the assumption has been made that the firmware is capable of BIOS booting and the processors are Intel with 64 bit cores.

An improved method of installing Windows 10 can be found here. This improved method does not require the use of the optical drive on the Mac.
Many early 64 bit Intel Mac models contained firmware which prevented BIOS booting from 64 bit Windows installer DVDs. Here, I will assume your Mac is one such model. This installation guide will explain how to use Grub to BIOS boot the 64 bit Windows 10 installation software.
Canonical explicitly developed a 64 bit version of Ubuntu for Macs of your vintage. Specifically, Macs with the following characteristics.

Use Intel processors with 64 bit cores.
Can not boot from optical media with multi‑boot boot entries.

This Ubuntu would install with a BIOS booting GRUB that could boot a 64 bit Ubuntu. Installers using this arrangement ended with Ubuntu 14. The memory requirements for Ubuntu 14 are under 3 GB. So, one possible strategy would be the following.

Install a BIOS booting 64 bit Ubuntu 14 Server, then use the included Grub to BIOS boot the current 64 bit Windows 10 installer. The installation of the BIOS booting 64 bit Windows 10 will replace Grub and Ubuntu 14 Server.

Here are the steps for implementing this strategy.

Download a BIOS booting 64 bit Ubuntu 14 Server ISO file. In this example, the file ubuntu-14.04.6-server-amd64+mac.iso was downloaded.

Burn the ISO file to a DVD. I used a reusable RW DVD.

BIOS boot from the DVD. Start up your Mac and immediately hold down the option key until the Mac Startup Manager icons appear. Insert the DVD and select to boot from the DVD icon with the label Windows.

Install Ubuntu Server. When an image similar to the one shown below appears, you can choose for the installer to add the parameter nomodeset to the linux command line. This can be accomplished by pressing F6 and selecting nomodeset from the menu. With Install Ubuntu Server highlighted, press return to continue.

If you internal drive already has mountable partitions, then an image similar to the one shown below may appear. If so, then select Yes.

When an image similar to the one shown below appears, select Manual.

When an image similar to the one shown below appears, select the line containing (sda).

Note: The existing partitions shown depend on how the disk was previously partitioned. Below is a example. Your disk will probably show different partitions.


When an image similar to the one shown below appears, select Yes.

When an image similar to the one shown below appears, select the line containing FREE SPACE.

Here you want to create a new primary partition at the beginning of the available space. When asked for a size, enter a new smaller size value. This value can be determined by subtracting 16 GB and the desire size of the swap space from the value shown. For this example, the desired size of the swap space was chosen to be 6 GB. Since the initial size was 137.4 GB, a new size of 115.4 GB was entered. The size value you will enter most likely will be different. Configure the rest of the partition settings as shown below, then select Done setting up the partition.

When an image similar to the one shown below appears, select the line containing FREE SPACE.

Here you want to create a new logical partition at the end of the available space. When asked for a size, enter the desired size of the swap space. For this example, the value was already stated to be 6 GB. You should enter the value you have already determined. Configure the rest of the partition setting as shown below, then select Done setting up the partition.

When an image similar to the one shown below appears, select the line containing FREE SPACE.

Here you want to create a new primary partition from the available space. When asked for a size, do not change the value shown. Configure the rest of the partition setting as shown below, then select Done setting up the partition.

For this example, the result is shown below. Select Finish partitioning and write changes to disk.

When an image similar to the one shown below appears, select Yes.

If an image similar to the one shown below appears, select Yes.

Finish installing Ubuntu.

Create a NTFS volume on the unused internal drive partition /dev/sda3. Since the new volume will be NTFS formatted, the MBR partition type needs be changed from from 83h to 07h. To make the change, first enter the interactive command given below.
sudo fdisk /dev/sda

Next, enter the following commands to change the MBR partition type.
t
3
7
w

Finally, enter the following command to restart the Mac.
sudo reboot

Enter the following command to NTFS format /dev/sda3.
sudo mkfs.ntfs -L WINSTALL -Q /dev/sda3


Install ExFAT filesystem support. Enter the following commands.
sudo apt update
sudo apt install exfat-fuse exfat-utils


Locate block devices for the internal HDD and the desired 64 bit Windows 10 installation ISO file. In this example, the file Win10_20H2_English_x64.iso exists on a ExFAT formatted flash drive. Plug the flash drive into the machine. The lsblk command can be used to list all block devices. For this example, the output from this command is given below. Since the swap is block device sda5, the internal HDD is block device sda. Since the flash drive is approximately 16 GB in size, the block device an be determined to be sdb1.
NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT
sda      8:0    0   128G  0 disk 
├─sda1   8:1    0 107.5G  0 part /
├─sda2   8:2    0     1K  0 part 
├─sda3   8:3    0    15G  0 part 
└─sda5   8:5    0   5.6G  0 part [SWAP]
sdb      8:16   0  16.6G  0 disk 
└─sdb1   8:17   0  16.6G  0 part 
sr0     11:0    1  1024M  0 rom  

If your determined different block devices, then make the appropriate substitutions in the following commands.

Transfer the Windows 10 installation files from the ISO file to a volume on the internal drive. In this example, the following commands were used. Basically, you mount, copy and unmount.

Note: The boot.wim and install.wim files are very large and therefore may take a long time to copy.

cd ~
mkdir winstall iso flashdrive
sudo mount -t exfat /dev/sdb1 flashdrive
sudo mount -t udf -o ro,nosuid,nodev flashdrive/Win10_20H2_English_x64.iso iso
sudo mount -t ntfs /dev/sda3 winstall
cp -Rv iso/* winstall
sudo umount winstall iso flashdrive
rmdir winstall iso flashdrive


Use Grub to boot the Windows 10 installer stored on the internal drive. Enter the command below to turn off the Mac.
sudo shutdown -P now

Remove the flash drive. Start the Mac. When the window shown in the image below appears, press the C key.

When the window shown in the image below appears, enter the following commands. This will boot the Windows 10 installer.
insmod part_msdos
insmod ntfs
insmod ntldr
set root='(hd0,msdos3)'
ntldr /bootmgr
boot


Proceed with the installation of Windows 10.

Create the partition for Windows 10. When you reach the window shown in the image below, select Custom: Install Windows only (advanced).

When the window shown in the image below appears,  leave Drive 0 Partition 1 highlighted and click on the Delete button. Next, click on the OK button in the popup window.

When the window shown in the image below appears, leave Drive 0 Unallocated Space highlighted and click on the Next button.

Proceed with the installation of Windows 10.

Install the Boot Camp Support Software (Windows Support Software). The Boot Camp Support Software is on the Snow Leopard installation DVD. The files can be accessed from Windows. Officially, only 32 bit versions of Windows can be installed on your Mac. Since I do not have your model Mac, I can not predict how difficult it will be to the adapt the software for use with a 64 bit Windows. You should consult lx07's answer for more information.
A Snow Leopard (OS X 10.6) ISO file can be downloaded from the website Mac OS X Snow Leopard Install DVD. You should verify the download by computing the SHA256 hash value. The Get-FileHash Power Shell cmdlet can be used to compute a SHA256 hash value. Entering Get-FileHash along with the path to the downloaded file in a Power Shell window should produce the following SHA256 hash value.
CBEEB2378C40B20A9B06236F567DE593E9030A0A865515B50CF6D35833E25CD5

Under Windows 10, the Boot Camp Support Software can be accessed by mounting this ISO file.

Remove unnecessary partitions and extend the Windows 10 partition. Boot to Windows 10 desktop. Next, right click on the Start button and select Disk Management. A windows similar to the one shown below will appear.

Right click on the last partition shown for Disk 0. Select Delete Volume…, as shown below. In the popup window, click on the Yes button.

Right click on the free space shown for Disk 0. Select Delete Partition…. In the popup window, click on the Yes button.

Right click on the partition with the volume label WINSTALL. Select Delete Volume…. In the popup window, click on the Yes button.

Right click on the partition with the drive letter C:. Select Extend Volume…. In the popup window, click on the Next button. Again, in the next popup window, click on the Next button. In the next popup window, click on the Finish button.

The result is shown below.

Exit the Disk Management application.


An Alternative: Installing Xubuntu

Note: I have no way to verify if these instructions will work for your model Mac. Based on the problems posted regarding the ATI Mobility Radeon X1600 graphics processor, I suspect these instructions will not result in a successful installation. Although, the problems seem to be associated with EFI booting and here only BIOS booting is employed. Even if the instructions do not work for your model Mac, users with a different model Mac may find the instructions useful.

First complete steps 1 through 4 outlined in the section titled &quot;Installing 64 Bit BIOS Booting Windows 10&quot;.

Locate block devices for the internal HDD and the desired 64 bit Xubuntu installation ISO file. In this example, the file xubuntu-20.04.1-desktop-amd64.iso exists on a FAT32 formatted flash drive. Plug the flash drive into the machine. The lsblk command can be used to list all block devices. For this example, the output from this command is given below. Since the swap is block device sda5, the internal HDD is block device sda. Since the flash drive is approximately 16 GB in size, the block device an be determined to be sdb1.
NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT
sda      8:0    0   128G  0 disk 
├─sda1   8:1    0 107.5G  0 part /
├─sda2   8:2    0     1K  0 part 
├─sda3   8:3    0    15G  0 part 
└─sda5   8:5    0   5.6G  0 part [SWAP]
sdb      8:16   0  16.6G  0 disk 
└─sdb1   8:17   0  16.6G  0 part 
sr0     11:0    1  1024M  0 rom  

If your determined different block devices, then make the appropriate substitutions in the following commands.

Transfer the Xbuntu installation ISO file to the unused partition on the internal drive. In this example, the following commands were used. Basically, you mount, copy and unmount.

Note: The xubuntu-20.04.1-desktop-amd64.iso file is very large and therefore may take a long time to copy.

cd ~
mkdir flashdrive
sudo mount -t vfat /dev/sdb1 flashdrive
sudo dd if=flashdrive/xubuntu-20.04.1-desktop-amd64.iso of=/dev/sda3 bs=1M
sudo umount flashdrive
rmdir flashdrive


Use Grub to boot the Xubuntu installer stored on the internal drive. Enter the command below to turn off the Mac.
sudo shutdown -P now

Remove the flash drive. Start the Mac. When the window shown in the image below appears, press the C key.

When the window shown in the image below appears, enter the following commands. This will boot the Xubuntu installer to a live version of Xubuntu.
insmod iso9660
set root=(hd0,msdos3)
linux /casper/vmlinuz
initrd /casper/initrd
boot



Install Xubuntu. The Xubuntu live desktop will appear as shown in the image below. To start installing Xubuntu, double click on the icon labeled Install Xubuntu 20.04.1 LTS.

Proceed with the installation of Xubuntu. For a brief moment during the installation, the following screen will appear with a warning message.

The above screen will quickly be replaced by the screen shown below. Here the same warning message appears, but is partially covered.


The intent is to install to the existing partition /dev/sda1.

Highlight the /dev/sda1 device, then click on the Change button. In the popup window, do not change the size value. Configure the rest of the controls as shown below, then click on the OK button.

For this example, the result is shown below.

Click on the Install Now button, then click on the Continue button in the popup window. Continue installing Xubuntu. When the screen below appears, click on the Restart Now button.


Remove the unnecessary partition and extend the Xubuntu partition. Press the key combination control+option+T to open a Terminal application window. Enter the interactive command given below.
sudo fdisk /dev/sda

Enter the following command to print the partition table.
p

For this example, the output produce by entering this command is shown below. Some of your values may be different.
Disk /dev/sda: 128 GiB, 137438953472 bytes, 268435456 sectors
Disk model: VBOX HARDDISK   
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: dos
Disk identifier: 0x0001b1a1

Device     Boot     Start       End   Sectors   Size Id Type
/dev/sda1  *         2048 225390591 225388544 107.5G 83 Linux
/dev/sda2       256716798 268433407  11716610   5.6G  5 Extended
/dev/sda3       225390592 256714751  31324160    15G 83 Linux
/dev/sda5       256716800 268433407  11716608   5.6G 82 Linux swap / Solaris

Partition table entries are not in disk order.

Record the value of the last sector occupied by the third partition (/dev/sda3). In this example, this value would be 256714751.
Enter the following commands to remove the first and third partitions, then create a new active first primary partition to cover the space formally occupied by both partitions.

Note: You should replace the value 256714751 with the value you recorded earlier.

d
1
d
3
n
p
1
2048
256714751
n
a
1

Enter the following command to print the resulting partition table.
p

For this example, the output produce by entering this command is shown below. Some of your values may be different.
Disk /dev/sda: 128 GiB, 137438953472 bytes, 268435456 sectors
Disk model: VBOX HARDDISK   
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: dos
Disk identifier: 0x0001b1a1

Device     Boot     Start       End   Sectors   Size Id Type
/dev/sda1  *         2048 256714751 256712704 122.4G 83 Linux
/dev/sda2       256716798 268433407  11716610   5.6G  5 Extended
/dev/sda5       256716800 268433407  11716608   5.6G 82 Linux swap / Solaris

Enter the following command to write the table to the drive and exit.
w

Enter the following command to close the Terminal application window.
exit

Restart the mac. Open a Terminal application window and enter the following commands. The first command will expand the ext4 file system to encompass the entire partition. The second command closes the Terminal application window.
sudo resize2fs /dev/sda1
exit



References
Apple MacBook Pro 15-Inch &quot;Core 2 Duo&quot; 2.16 Specs (Late 2006, MacBookPro2,2)
Apple MacBook Pro 15-Inch &quot;Core 2 Duo&quot; 2.2 (SR) Specs (Mid/Late 2007, MacBookPro3,1)
Apple Introduces Boot Camp
Setting Up Boot Camp
Install Windows 7 on your Mac using Boot Camp
About EFI and SMC firmware updates for Intel-based Mac computers
Boot Camp - Windows XP Drivers Update 2.1
Boot Camp Drivers Update 2.2 for Windows
Boot Camp Software Update 3.1 for Windows 32 bit
Boot Camp Software Update 3.1 for Windows 64 bit
Boot Camp Software Update 3.2 for Windows 32 bit
Boot Camp Software Update 3.2 for Windows 64 bit
Boot Camp Software Update 3.3 for Windows
Partition type
“Select CD-ROM Boot Type:” error during Windows install
Oscdimg Command-Line Options
Ubuntu 14.04.6 LTS (Trusty Tahr) Releases
Booting 64-bit Ubuntu Images on a First-Generation Mac Pro 1,1