a wireless mouse?

And why is this option to disable, "exit on mouse movement' necessary if you are turning the mouse off?

Sorry but I'm just intrigued.

Finding screensavers like you wish is going to be difficult as that sort of option isn't always given in reviews, and I don't know of any, but good luck with your search. Just beware that screensavers can also harbor malware, so make sure you scan them thoroughly before installing them.