I don't see what's stopping anyone from RPing a mute/deaf character as is. We even have sign language for it.
Once got admins on my case for playing a mute character in a not-important role.
That really doesn't make any sense, I mean if you are a non-important role, there really isn't a reason that you wouldn't be hired if you could do your job. Also, I am pretty sure I have seen a few characters that either couldn't speak or talk.