Hi Meg,
I don't know of any varnish, as the hard surface of the papier mache alone would probably play havoc with wearer's face, especially when they're working up a sweat!

How about soft foam pads stuck at strategic spots on the inside, to keep the mask proud of the face, something like the ones you get inside cycle helmets, so that the hard surface doesn't actually come in contact with the skin?

Hope this is of some help.

Zyggy