Both options have their drawbacks. If you were to ask me, I'd say you should just buy some dry ice. You can get it from a lot of places. It is easily attainable at any party-supply store. Even Wall mart will probably have it. Unlike actual smoke, it's odorless, and it doesn't need a fire source to catalyze, plus its not as hazardous as smoke when you inhale it, and trust me, you will end up inhaling some of those fumes.
Your only real challenge is designing a trap that will accommodate the dry ice. You'll have to make the prop waterproof, which means there can't be any way for the water inside the trap to escape, but at the same time you need a way for the dry ice smog to escape from the trap . . . and you have to handle the dry ice itself with care, because it can give you freezer burn or worse if you handle it with your bare hands. You should also have some pores made in the trap body so the faux-smoke will escape in all the right places. There's really no need need to employ any other elaborate forms of half-assed chemistry.
Should you use the smoke bomb method, then at least put some metal plates along the inner walls of the trap so you don't risk putting any burns insides of it, and try not to breath that stuff in . . . unless you enjoy that sort of thing.