HI, I groom cats/dogs, and you have the right idea with the metal comb. The only better suggestions I have is 1) a narrower tooth comb or a shedding comb (one with alternating long and short teeth-my personal favorite) and 2) just pull the mat out (instead of cutting). We (at the grooming shop) never use scissors on a cat. The shaving of the belly with a clipper is a fantastic idea.