I don't know about the cleaning part of it, but the mask on while walking around and mask off while using the equipment is what most / a lot of folk in my gym are doing and pretty much what the law in Scotland says, providing you think it's reasonable that while doing exercise a face covering shouldn't be worn, which I do:
"5.—(1) A person who enters or remains indoors within a place listed in regulation 6 must wear a face covering, unless the person is—
(r)taking part in exercise of a type which reasonably requires that the person is not wearing a face covering"
https://www.legislation.gov.uk/ssi/2021/277/regulation/5
It seems like I'm going over old ground here, and I'm really not Jason Leitch, honest, but I guess it's about reducing the quantity of covids flying around, not eliminating them, while letting people do the thing that they are in the place to do. It's also why you can have your mask off while you're supping a pint but you're supposed to have your mask on while you do your messages - the mask makes the former impossible, but not the latter.