Anyway, this remote mouse has continued to wake up the PC, if the mouse was accidentally knocked or moved.
Obvious solution was to go into Control Panel, and only allow the main (wired) mouse to wake the PC, and to stop (mouse > power management) the wireless one from doing that. Just didn't work, though.
Yesterday, found the soloution here - and it is slightly surprising, simple, and has worked a treat:
https://www.youtube.com/watch?v=75BpfWq ... l=SoSoTech