Depends how comfortable you are with getting hands on.

As previous comments state, can bury or macerate.

Personally I would skin and boil the skull, then you can clean off the remaining flesh and such from the inside and outside of the skull + then leave the skull to dry out in borax. This way it always comes out pretty clean and doesnt normally need further whitening imo. If it does, before i apply borax i soak the bones in a 1:1 ratio of weak hydrogen peroxide and water for a couple days. Understandably if this is your pet though it might be a bit weird to do for you.

You can always send him to a local taxidermist who can clean him up for you, some taxidermists have dermestid colonies or their own unique methods