Why ‘without removing them’?
I always remove the keys: it's much easier to clean them, and doesn't risk doing any damage to the important bits.
I use a blob of
Blu-Tak to remove them. Knead it until fairly soft. Press down firmly on a key to cover it, then lift it up sharply: the key will usually come away with it.
It's a very safe method; I've used it over the years with all my Psions (which have almost identical keyboards), and never done any damage. You have to be careful with the space bar and Enter keys, as those are attached to metal bars; but all the other keys can be easily removed, cleaned together, dried, and replaced.
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And to confirm what salvomic says:
If for whatever reason you really don't want to remove the keys, then IPA (isopropyl alcohol, i.e. isopropanol) is probably the safest in-place cleaning agent: it's non-toxic, dissolves oils &c, evaporates quickly without leaving a residue, and won't damage most electronics.
This type of keyboard is made by using a laser to heat parts of the black plastic so that it turns white (and expands slightly). So there's no print to rub off, and it's OK to scrub the keytops (as long as you don't do so hard enough to erode the plastic itself).
(If the lettering goes dark, it's probably due to grease, dirt, and oils from the fingertips. I
think that those can be absorbed into the plastic if left for a long time, so it's probably a good idea to clean the keys from time to time to prevent that.)
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Also, I'd recommend learning to touch-type if you can (though that might be easier on a full-size keyboard). As well as not needing to see the keytops, you'll be able to type faster and more accurately, and if you're copying something you won't need to keep looking away from it. You don't need any formal lessons: just rest your hands comfortably with your fingers over A/S/D/F and J/K/L/semicolon. Work out which finger is most comfortable for each of the other keys (e.g. your left middle finger is probably best for 5, R, D, and X), and then practice typing using only that finger for that key. It feels strange at first, but it soon becomes a habit.