There were different types of material used for keytops through out the last 150 years or so. Ivory, celluloid, plastic, all now in varying condition. So, what may work for one will not always work on another. Then there is the problem of the sharps, so you are really cleaning two materials at once unless you remove the keys and do them separately. Sharps have been made of ebony or dyed birch and other materials I am sure as well as plastic. The wood often has a dye or finish that can smear onto the whites when cleaning, this usually is not a big problem and can be cleaned up as you go.
Yamaha had a big problem with this on their "Ivorite" keyboards, the whites became permanently stained black from the sharps simply through normal playing.
After trying everything I could buy, make, or think of, I have returned to what the old timers showed me way back when I was just getting started. You will need a mist bottle purchased at a beauty supply store, one that has a pump top that gives a very fine mist, add a few drops of dish soap, then fill with water. Apply a mist to the top of the keys and wipe with a dry cloth. If the cloth turns black from the sharps, try to use a different part on the whites. If the keys feel sticky, let them dry before playing. This will not hurt the finish or any thing else I can think of, but, I would be careful not to get it on the strings or tuning pins.