For an open wheel a lot of people use this one, which is silent. It's a good wheel - our syrian had it (I had it screwed upside down in his cage). It's not expensive but ideally you need to paint the inside with plastikote.
Like everything it's gone up in price - it used to be about £11. And now £16. They're good wheels though, they have a cork running track which is nice for their feet. It has ball bearings and is silent.
It's not a big deal to paint the inside with plastikote - takes about 10 minutes, dried in a few hours. Most people do a second coat. It means it's then wipe clean and not going to get stained and stinky. Not all hams pee in their wheels but just in case.
Most of them like the enclosed wheels with the holes, but not all. The nice thing about the open wheels is they can jump out easily and flop on the substrate (ours used to like doing that). A pot of plastikote costs £4 and the small pot goes a long way - you'd use less than half of it painting the inside of the wheel - it can be used on any wood items to make them wipe clean.
Trixie Wooden Exercise Wheel | Free P&P on orders PS39+ at zooplus!
This is the plastikote. It also comes in colours if you fancy a coloured wheel and painting the whole wheel (I just paint the inside as the outside is fine unpainted).
Plastikote B26W 59 ml Enamel Paint Bottle - Clear : Amazon.co.uk: DIY & Tools
You could keep the plastic trixie wheel for a playpen item maybe = with the front on. I don't think I'd be too happy with the spindle exposed. He might use it fine with the front on in a playpen as not his main wheel.
I wonder if he's had an open wheel before and just prefers it.