No question about it let it hang,, as long as it's cool and well ventilated. A week may be excessive for a deer 4 days should be sufficient just keep an eye on it. If it starts to get to smelly get it cut up but if it stays clean smelling you have nothing to worry about. I usually try and hang my moose meat no less than a week but like I say deer maybe because it's smaller seems to come along quicker. And yes you will lose some to drying, like between the ribs will be lost and the fringe areas but no biggy it's scrap anyways and take out the tender loins as well as you will lose them in about 2 days if not. Just make sure it's spread open wide and not touching another animal and has good good circulation and it's the best thing for your meat.