How to shutdown or reboot HP Pro Slate 12 tablet without power button? Is there any way to shutdown or reboot HP Pro Slate 12 tablet without using the power button?

I'm afraid the button will wear out quickly, so I'm looking for a workaround solution.

Yes, I know that for rooted devices there are a lot of shutdown and reboot apps, but it is impossible to root this device. It has Android 5.1.1.
Provided that HP has not messed up with AOSP much in your device, you can use Tasker with AutoInput (both are paid apps with 7 day free trial) to reboot/shutdown without using power button and without requiring root access.
In essence, what we're going to do is show the power dialog (the one you see when you long-press the Power button).
(Solution tested on AICP ROM (Android 5.1.1))
Instructions

Install both the apps and enable accessibility service for both from Settings → Accessibility
In Tasker, create a task with the action: Plugin → AutoInput → Global Action →  Configuration → Action → Power Dialog
Go to Home screen → find the option to add Widgets → select Task Shortcut → choose the newly created task → select an icon

An icon would now be placed on your home screen with name as the task name and icon that you selected for the task. Tap it and the power dialog would show up.
(Click image to enlarge)

In case you want to have a functionality of launching that dialog from anywhere in the system, you can consider LMT Launcher.
My answer for Page up and page down in web pages and elsewhere will help you in its basic know-how.