Cheap flea combs sometimes don't work, if the fleas are slipping right through the comb go buy a better comb. Just set the cat down and comb him, often it is a very satisfying chore for both parties. Just wash the fleas down the sink or put them in a container of soapy water. A flea comb is really the only product that can be used on kittens. While flea combing won't eliminate a flea problem, it can reduce the numbers to a point where at least the situation is bearable.
Flea combs are completely non-toxic.
If used carefully and thoroughly these will eliminate the fleas on the cat. I recommend them if bringing a cat into a flea free environment. It is often a good idea to have this professionally done at a reputable place. If flea collars really worked well, there would be no need for other flea control products. I have never had much luck with them nor heard of anyone who has.