At our camp, we do it all ourselves. You can leave a deer for a while if it's cold enough, by why bother? Skinning is much, much easier when the deers body is still warm. It peels right off. Skinning a cold deer can be a huge pain.
Don't be too worried about messing up those straps. They're not hard to remove, at all.
Better you nick your straps and hams up a little than drop the whole thing off at a butcher where it'll be run through band saws and whatnot.