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So after the hide has sat with the eggs on it the eggs are then washed off the hide and the hide is worked until dry then smoked later, is that right? That's what I've been doing but I've seen videos of people smoking with the eggs still on (??) and wondering if I'm doing it wrong!
Aluminum foil would break up over time and become a mess, waxed paper would break down. You could try coating cotton canvas in beeswax (sprinkle beeswax over fabric, heat, then brush the wax over it) but I'm not sure how long it would last.
It's really easy to find dead squirrels just lying around by the way, you can't be barbaric to something that's already died. I would *find* (not kill) dead squirrels, pelt them to make little moccasins for my baby's feet and feed the meat to my dogs. Barbaric? No, if you want barbaric check out where most storebought meat and shoes come from