Sorry it ook so long to reply. Ironicly, I've been bear hunting. Some good info on here. In my opinion, the beatles are the best. Like mentioned before, they get in all the little nooks and crannies and it sure looks nice when its done. I have quite a bit of experience with taxidermy and, to be honest, its well worth the $60 to send the skull off to someone with dermistid beetles. If you don't want to spend the money, or just prefer to do things yourself, I always boiled in water with some baking soda thrown in. I've heard of people using the dish soap but I've never tried it other than squirting it in the brain cavity and letting it soak for a bit before rinsing it out with hot water. I like to boil the skull awhile, then pick awhile, then boil a little more and so on. This helps keep me from overboiling. When you are picking the skull, be sure not to cut down into the bone because it WILL leave marks if you're not careful. You don't have to baby it but just be sure not to cut into the bone. I use a wire coat hanger or similar and water to remove the brain. There is always little bits that hang on and are a boogar to get out so be patient and thorough. Those little bits will leave grease spots on the outside.
I, too, prefer the peroxide over bleach for the same reason mentioned. It also does a nicer job, in my opinion. Like was also mentioned, don't get it on your skin unless you want white skin. No kidding, it will turn as white as snow. Trust me, I know. lol It burns, too. Just wear rubber gloves.
For the claws, just pick everything you can off. I like to take a scalpel and trim everyting possible off including the cartilige.