I too was having issues with the mouse and vince's solution did actually work for whatever arcane reason. Thanks vince!
Edit: Actually I had a closer look and the reason his solution works is that when copying the folder the executables lose their compatibility settings. I had a look and they are installed with Win95 compatibility checked, and turning off this compatibility completely fixes the mouse lag!
Does anyone know how to use this solution if we installed the game using GOG Galaxy? In that case, both executable files have the compatibility setting locked to Windows 95, with the checkbox greyed out so it cannot be disabled or changed.
I know I can simply use the backup installer package, but I'd like to know how to get around this while still having the Galaxy features available.