1) Keep a big black heavy duty trash bag in the back of your car.
2) keep a pair of heavy duty work gloves with the bag.
3) NEVER pick up road kill with your bare hands.
4) Make sure the road kill is dead-- poke it with a stick before attempting to pick it up.

I know that last one sounds obvious, but a wounded or dying animal will defend itself if at all possible. BE CAREFUL.

Finally, before you set out on a road kill safari, find a local taxidermist who is willing to receive, skin, and treat the hide unless you possess these arcane skills, yourself. Talk to the taxidermist, tell him what you are going to do, seek and follow his advice.

Finally, a lot of taxidermists (at lease here in the Shenandoah Valley) regularly pick up all sorts of road kill, skin 'em and sell the pelts. Locally a good skunk pelt runs $20-40 dollars, ready to go.