MacBook Pro (13-inch, 2017, Two Thunderbolt 3 ports) running Mojave (10.14.3 (18D42)) is does not recognize external boot drive
Your guess is correct. The 2017 model Macs can only EFI boot Windows. Since the first partition on the external drive starts at sector 2, the drive does not have the space to convert from a MBR partition table scheme to a GUID partition table (GPT) scheme. This means you would need to restart the installation process.
When installing Windows 10, I would recommend you do not use VirtualBox. This recommendation is based on the fact that the Windows 10 ISO from Microsoft and the Windows Support Software from Apple contains all the software required to install Windows 10 to your external drive. Therefore, there is no need to use a third party product such as VirtualBox.

The use of a virtual machine to install Windows dates to when Mac owners removed the optical drive so another HDD or SSD drive could installed in their Mac. After the optical drive was removed, often an owner would discover the Windows 10 installer could not be booted from a flash drive. This led to the use of a virtual machine as the only way to install Windows other than change the hardware configuration.

Since you model Mac can EFI boot from either an internal or external drive, you do not need to use a virtual machine. However, if you wish, a virtual machine can also be used. Below are some references to previously posted methods for installing Windows 10 on an external drive.
Drivers not working on Windows 10 installed (CLI process) on external SSD running on Macbook
Is it possible to use Boot Camp with Windows 10 from an external HDD?
How can I copy the drivers provided by Apple when installing Bootcamp on an external drive?