I have always heard to clean pots with "tuner cleaner" available at most stores that sell electronic stuff. You may not need to disassemble the pot to use it. I think it was originally intended for the old TVs, hence the name.
Taking a controller apart will void the warranty. Taking a pot apart may void your sanity.
This is probably not something to recommend to a beginner.
CH Products controllers have pots removable without a soldering iron so a user could replace them, and the connection is occasionally flaky resulting in the output wandering around when it shouldn't. Crimping the connector will work, but getting it replaced under warranty is better. I sent a joystick back to Amazon when this happened and they replaced it without question.
Hook