Thanks to sdRohan I learned about the Group Policy folder in the Start10 program folder. The FAQ he cites applies to PCs connected to a domain, but the PCs I'm dealing with are in a workgroup. Fortunately, they are running Windows 10 Pro so GPEDIT is available to me. Here's what I ended up doing.
I copied start8_gp.admx from:
"C:\Program Files (x86)\Stardock\Start10\GroupPolicy\start8_gp.admx"
I copied start8_gp.adml from:
"C:\Program Files (x86)\Stardock\Start10\GroupPolicy\en-us\start8_gp.adml"
Then, in GPEDIT I found and opened:
User Configuration> Administrative Templates > Start8
Here’s a list of all the possible Start10 GPOs.
The two I wanted to remove from the Start button's context menu were:
- Allow access to config user interface via the right click menu (disable)
- Show shutdown option on right click menu (disable)
I would have liked to also hide the All Programs menu but that option appears to be unavailable.