Use a serial mouse? There are probably bundles of 20 being sold on e-bay hehe. There are adapters too.
You could more than likely find a bin full of old serial mice at a warehouse somehwere. I remember when it was only serial mice, then came ps2 and usb... Microsoft serial mice were pretty good, pre-optical, and the bottom cover comes off easy for 'ball cleaning.'
I'm sure there are adapters, so you can get a ps2 to serial adapter or a usb to serial http://www.cablesnmor.com/usb-serial.html
for the newer mice. I just looked in my inventory, don't have one - just 3 usb to ps2, otherwise I'd post you one.
The other option you could go (but I don't know about compatibility with an unkown older machine) is to get/buy an usb add-on card to plug into the motherboard, and run the mouse of that? I'm just guessing it would work with an unknown old machine, but it is at least running an OS that woud likely support it.