My Chineseys have been terrible for peeing in their wheel but I tend to look at it this way, it's better done there than in their nests.
I'd avoid washing it out too frequently as that can actually make the situation worse. They seem to like it being a bit gross and I guess as their eyesight isn't great, they know it's theirs. What I tend to do when I wash Jessie's wheel is rub some of the substrate from her cage in the wheel so that hopefully some of her smell will transfer on to the wheel.
Congratulations on your new hamster by the way!
