You can not bleach plastic whiter than the original colour.
The only way to get something that was not pure white to begin with to become white is to paint it, but that is feasible only for the case. The top of the keys take a lot of wear and the white paint will wear off sooner or later and that will look worse than pure beige keys. Besides, the paint would cover the legends.
My suggestion for you is that you paint the case white and start looking a new set of white key caps, if some could be available for your type of keyboard. Cherry MX compatible caps are available from several sources, but not super-easy to find.
I am in the process of painting a keyboard case myself. I have opted for white on the case and to dye my keys dark grey or black (blank keys) using RIT Dye.
I have never been able to get hold of white Vinyl Dye spray, but I am very interested in seeing how good the result can be.
I have been recommended to use Krylon Fusion spray paint because it is known to have good properties for plastic. Unfortunately, I can not find any in my area, so I have to use both primer and paint.
Unfortunately, with paint, you will lose the coarse texture on the plastic. It will become smooth.
The result of a paint job depends on a lot of things. First of all, the preparation job is important. Disassemble it completely, remove or mask (with masking tape) and decals and rubber feet. Clean each part and rub it down with alcohol. Then when you paint it, follow the instructions on the can(s) to the letter. Don't be impatient.
Use the same brand of primer and top coat if possible -- the wrong combination may crinkle or crack... perhaps first after a month. Spray many light coats -- the first coats don't have to cover everything. If you paint it too thick then the paint may run, or perhaps not even cure properly .. ever. If you use primer, let it dry and harden for at least 24 hours before painting the top coat. If you can smell it when you put your nose to it, it is not ready yet. If the coats of primer, when cured, are a little bubbly, then you can use fine wet-and-dry sandpaper to get a nicer finish, but tbe sure to clean and dry the surface well before painting.
I mention a lot of mistakes that you can make.. but that is only because I have made them all myself on previous projects... :-) Good luck!
