You can't just connect a different cable. The signals on the cable will have to be USB signals.
It you could fit the electronics from an active PS/2-to-USB adapter in there, then that would be great, but I am afraid that there is not enough room.
The difficult route would be to replace the controller, maybe with a Teensy. If I remember correctly, the pitch of the traces of the edge connector is 1/10", which is the same as on a regular
stripboard. You could base your firmware on one of the available Teensy-compatible firmwares that you could find on this board, but you would have to modify the code to know the specific matrix of the IBM Model M2.
Anyway.. Would it be worth it? If you use a USB port on the back of your computer, you wouldn't see the ugly (?) PS/2-to-USB adapter anyway.