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Peeing in the wheel is totally normal behaviour for hams, not all do it but many do even if they also have a pee spot elsewhere.
Wooden wheels do need to be protected before use though, you can use Plastikote water based enamel which is safe & non toxic, give the wheel at least two thin coats to water proof it.
Don't take his wheel away, they really must have a wheel in the cage.
You will never get the pee out of wood so you may as well just leave him with the one he has now & get a replacement & paint that.
Alternatively you could get a good plastic wheel, the best is the silent runner (not silent spinner!) which is easy to clean.
When you have either a painted wheel or a plastic wheel don't over clean, the more you clean the more they pee in it usually! Once a week with warm water, no cleaners or disinfectants with a strong smell, is enough.

How long have you had him now & how much cleaning have you been doing? If you clean too much he won't be able to scent his cage & they do need to have their scent all around the cage, if you clean too much they will scent mark a lot but it can also lead to them peeing in more than one place.
Best to just spot clean pee & not clean anything else or change the substrate for at least the first few weeks, if you have a litter tray in a corner of near the house (even in the house if it's a good size) you can keep adding some peed on substrate to encourage him to use that, even when you spot clean pee it's a good idea to leave a tiny bit of the used substrate so the scent stays in the appropriate area.