I haven't kept any skins for years but I can tell you this much regarding fleas and the following works for any wild game such as rabbits or squirrels:
Once you have your kill leave it on the ground somewhere around the hunting area for 30 minutes to an hour. Once the body temperature drops a bit the fleas......uh, flee.
In general fleas and ticks know when something is dead by the body temperature. As soon as that temperature drops they're off to find something else to feed on. Leaving your game in the field a bit makes it more likely that the fleas and ticks will leave to feed on other wild critters rather than the family pet or family itself.
