I had this situation with a Logitech wireless keyboard/mouse combo as well, that also used a single reciever. I used a Belkin USB KVM, and plugged in a PS/2 -> USB keyboard converter into the other port to simulate having it occupied (i.e., the converter wasn't connected to anything other than the KVM switch). This enabled it to work properly. However, I seem to remember that things were funky when I rebooted - which wasn't very often, so it worked OK for me.
FS