I doubt your fan and light are on two separate breakers. It's more likely you meant to say they're on two separate switches.
If they really are on two breakers, they must be controlled by two separate switches, or you might re-wire it to feed one of them from the others switch, which would essentially be moving that load to the other breaker, and may negate the need for one of those breakers.
As for how to do the work?
If the wall is clear and unobstructed on the opposite side of the wall where the current switch is, you may be able to remove the switch and protect the wiring, then very carefully destroy the box piece by piece, around the wiring using a drill and sawzall.
Then cut a hole on the opposite side of the wall lining up with where the original box was, and install an 'old work' box there, threading the wiring into it.
Then patch the hole where the switch used to be.
Reinstall the switch or switches that were in the box, and enjoy.