If they are for human consumption, then gutted on the field, skinned once home. Anything else i'll do next day.
Buy a cheap box of latex type gloves, like tattooists and mechanics use and a plazzy bag. Gloves on, gut bunnies, leave guts for critters, gloves in bag and home to bin. Gloves again to skin at home.
Dont half save on stinky hands on steering wheel and house.