When I make up a batch of raw one of the ingredients is raw egg yolks. Raw feeding experts recommend NOT feeding raw egg whites because it depletes the body of something that I can't think of right off the top. One a week won't hurt, though. If you're thinking of salmonella, that's not a problem for cats (or dogs, I take it).
If your objective is a glossy coat, get those eggs with "Omega-3"