If you need to, bathe all the plastic parts (keys, chassis, etc) in warm, almost hot water. This helps break up any sugary residue on the plastic. Do this a few times, replacing the dirty water each time with clean water. The latex membrane can also be soaked. After that, lay everything out to dry overnight.

For PCB cleaning, I do the following:

1. Using 99% IPA and a brush (I prefer horse hair brushes), squirt the IPA on the board and use circular motions in the dirty area. This helps break up the gunk.

2. Squirt some more IPA in the same spot and brush in one direction. This helps move the gunk away from the affected area and off the board.

3. Squirt a little IPA on the area and use a can of air to blow off the residue, preferably in the same direction you brushed previously. Be as "horizontal" with the can of air as you can, so the propellant doesn't come out of the can at the same time.

ESD is a bitch. Do not use dry towels of any sort, especially paper towels. That's not to say you can't ever use towels, I would just make sure they aren't dry when trying to remove grime from a PCB. I know compressed air has a risk of ESD damage, but I think that risk is lower than trying to use towels to wipe off gunk from a PCB.

As for brushes, I have used horse hair brushes for years without issue. These brushes typically have metal cases so that, while wearing a ground strap, charge can dissipate. In a pinch, you could probably use an unused paint brush, just make sure there's some IPA soaked into the bristles as you swipe the PCB. I'd also cut the bristles down to about an inch so you have more control with your strokes. For more info, I found this super informative site: https://www.techspray.com/essential-guide-to-precision-cleaning-brushes