Multi-workstation Mouse

If you have two computers at your desk, as many people in engineering or design do, you probably have a keyboard for each and a mouse for each. (I'm leaving out keyboards for now, because I'm under the impression that they work in a different way than the mouse.) I've had three monitors in a row, (two UNIX, one PC) and spent interminable stupid-minutes wondering why the cursor, which drifts happily over the gap between UNIX 1 and UNIX 2, wasn't moving across to the PC screen no matter how hard I banged it against the side of UNIX 2 (the cursor, not the mouse - that's a different idea).

You may have already got yourself a cordless mouse for one or other of these computers - presumably they 'talk' to the relevant box in the same way, so how difficult would it be to use the same mouse for both? They could do this with a reasonably stiff scroller or switch on the side at about thumb position. Just like a multi-appliance remote for TV/video etc, you flick the switch and the mouse is applied to UNIX, flick it back and you are on your PC.
If you don't want a cordless mouse (I don't know - you lose things easily? people pinch things from your desk?) the same switch could work by deciding between two cables, which are together in one casing until they split about 1 metre down the line and become two discrete cables; since you may have your workstation box at the other end of your desk from your PC, there may be a need for much longer cabling. Still reasonably messy but you only have to hold onto one mouse.
The software for this would probably be even easier to write if the two (or more) parent computers weren't running on different OSs - having one cordless dual mouse for your desktop and laptop would be (I think) desirable. I would say that a three-parent mouse (workstation+PC+laptop) would probably be the maximum you could expect though, any more and you could just end up going round the office confusing other people's computers...