If you did a standard install of ME, I'd expect it to have dropped the .CAB files somewhere on the system drive. If they're there, even the rather rudimentary PnP in WinME shoud be able to find a mouse driver if you just go into Device Manager (or whatever ME called it), uninstall the mouse, and reboot. You might not get the best possible driver for a particular fancy mouse, but it should give you basic mousiness. If the .CABs aren't there, it should ask for a driver/system disk that you probably have that should have the generic ones on it.
I'm going by my recollection from Win98SE days, which were a long time ago, but I think that's what we used to do ... .