What’s the best way to clean the MSX keyboard?

Depending on the state, if it is just dust (and this is not specific to the MSX), is to take a canister of compressed air. Take the keyboard/computer outside and just blow it out.

If it is more then just dust, for example some spillage that causes the keys to stick, you need to get underneath the keys. I don't know if the key-caps of the WSX can be easily removed, but that is what I have done on occasion to PC keyboards. After that just clean it with a cloth and a gentle soap, making sure you don't leak anything into the system itself. Cotton buds can also be useful for tight spaces.

Kitchen Clean Wipes. With or without the lady above.

On a Philips model, keys can be removed and cleaned quite nicely:

Each key has 2 plastic pins (one left, one right) keeping it attached. The trick is to -gently- press 1 pin with a screwdriver until it gets out ; then you simply pull the key.
On your model, it will be different, but all keyboards have their method. Try with an easy key you don't use often - when in doubt, don' brute-force. Try to put it back in place, verify it works again -before doing other keys.

As Alexey says, Kitchen Clean Wipes are the way to go. They don't "leak" so much and smell nice. At worst, try Demineralized Water on a piece of (non-fluffy) cloth.

Nice tool, indeed ! So this exerts pressure on both sides at once ; definitely a must-have.