I found, through trawling the Microsoft answers page referenced above, this excellent app called Windows Cursor Hider.
According to the manual, the app:
"...is a small script written and compiled using AutoHotKey that hides
the windows cursor when a user starts typing any alphanumeric (and
certain coding-related) characters, and shows it again as soon ...
To do so manually in the Registry:
Locate the context menu item in HKEY_CLASSES_ROOT\CLSID, e.g., fro Run as Administrator:
You will likely need to take ownership to make any change to that key.
Add a DWORD value, flags.
Set the value to 0 to put it in the Rename section of the context menu.
Set the value to 1 to put it in the Send to section of the ...