You can get mechanical mouse mover devices that are not connected to the pc at all. It should be fully undetectable.
(This is going to make me embark on a weekend project to use an Arduino, some servos and a 3D printed finger to move my trackball.)
The trick that I heard is to just place the mouse on a clock. The second hand jiggles the mouse every minute. Can be stashed away in a drawer or something. Never tried this though.