Isn't that like mixing Hydrogen Peroxide with OxyClean or something like that?
Yep. Oxy Clean contains more hydrogen peroxide (in a powder that turns into it when it gets wet) and the initiator.
The initiator is called TAED, and allows h202 to work in room temperature.
To bleach keycaps, you use only hydrogen peroxide and oxy clean - no thickener. You don't want the detergent to foam too much.
UV light makes h202 work. It is in sunlight. How much time it takes depends on how yellow it is and how strong h2o2 solution you have.
35% h202 is NOT low strength - that is very high. Low strength is using a hair bleaching kit that is 6% or so.
If you bleach it too much, some plastic will turn white - which you don't want.
Do use gloves and eye protection when using h2o2. When diluting, always pour the concentrated solution into water - not the other way around: if it would splash, the splashed droplets will be water, not concentrated h2o2.