Why tumble them? It is just mud (I think, since you did not describe their current condition). Could you just wash them, rinse them? I would not use soap, as that might let water infiltrate into the cases, but if I could avoid tumbling, I would.
I would not avoid tumbling if it seems necessary. A 22 going off unconfined in a chamber is not so large an explosion as to represent a danger to life, but could present problems, especially if it sets off other rounds. The most likely worst thing to happen is that rounds and tumbling media might be scattered around the room. A prudent precaution would be if you cover the tumbler with a blanket. Even if it is outside, you wouldn't want to lose any live 22 rounds.
I would use less energetic cleaning techniques first and go from there.