Just from reading the rulebook, I can't see any reason why a mask couldn't be allowed, so long you still have protruding lower teeth and your face (and maybe neck?) is mostly or entirely green, but whatever you come up with should probably be shown to a marshal or two before you bring it into game, and prepare for having to do makeup if it doesn't quite make the cut.
It might be a bit more awkward to eat with a mask on, too, and you're probably going to be way hotter and sweat more in a mask, so you might want to take that into consideration if it's a non-allergy reason you'd like to avoid makeup.