There are lots of ways to accomplish this. With a wireless mic, you either will have to route the audio back to the stage, or create a remote switching system.
Setting up a remote relay system would be pretty simple to do. In that case, a failure of the connection to the stage would maintain normal FOH audio, and all of the audio remains near the same path.
More complex solutions involve a button that controls your mixer to mute/unmute properly. This would mean less in line of the audio path and as well would mean a visual indication on the board as to what is happening with override available if needed.