When I whitened my keys, I used two clear plastic cups per 2 keys.
Place the first cup, place in 2 keys (or however many that fit easily upright), pour in Hydrogen Peroxide, place in second cup (to squish the keys), and rubber band the cups together. A bit tedious and the cups I used only fit 2 keys each, but it kept those things in place.
ALSO, please note that many clear plastics still block UV light. Check with a blacklight or something. If in doubt, I know plastic wrap doesn't.