Whenever I go somewhere and have to touch stuff, the only thing I’ve found to do is just not to think about what I’m doing, or else I get super stressed about it and, like you said, want to “clean” it.
I’ve tried similar things to the evaporating thoughts, and it’s seemed to help a little, but it sounds like it’s a lot worse for you, sorry.
I’ve never had someone suggest sports to me, but I would probably have about the same problem with it as you do.