Hamster wheel bearings collect dust fast. That causes the squeak during quiet times like recordings. A quick fix might work, but replacing the wheel is better.
A buddy of mine shot a commercial with a macaw that would not stop yelling. They ended up making a deal with the bird's trainer where the parrot got a peanut after every clean take. It sort of worked, but they went through a whole jar of peanuts and the bird started squawking for a nut before they even said action. The footage was usable, but my friend said the whole crew was cracking up by the end of it.