I recently did a simple test just using primer and a few layers of newspaper as a skin. We're about a month into the wet season now and it's borne the brunt of it with no sign of degradation whatsoever. I haven't given it a "hammer test", but I think would be plenty rigid for a skin, especially when applied to both sides of the foam. Were I planning a trip over Niagara Falls, I wouldn't build a barrel out of it...but a foamie ? Sure.
That's with 3 plies of newspaper: if you could get it completely saturated, a heavy paper would probably make a great skin. You would need something pretty runny and multiple applications means that it would stick well to itself: 'the mix' would probably work pretty well.
I also tested out some
Ram Board (floor protector paper), which is thicker but less dense than kraft paper, and couldn't get acetone-thinned epoxy to penetrate all the way through (though vacuum infusion would probably work).
Given what it's produced for though, it's no surprise that it was more difficult to wet out ("Exclusive Spill Guard™ technology")