Bet you're younger than me
That wood one I linked from Zooplus works well in the HH. It has quite a sturdy base so can either just stand in the cage - or - as I did - screwed it to the top bars upside down. Which means it saves space and has a little bit more space underneath for substrate. Also keeps it quite stable.
Now this used to be easy to achieve. Underneath the base are two screws which you remove. And at one time that released the wheel stand from the base. But these days it seems well and truly glued to the base, even with the screws removed - and last time I had to get OH to part saw the base off.
Anyway once you've got the wood base off, you just use two large washers on top of the cage, put the screws through the washers and the top bars, and screw them back into the holes in the stand that they came out of. It's a quick easy job (once you've got the base off). The only fiddly bit is holding the wheel while screwing the screws in - easier with two people - one holding the wheel in place while you put the screws in. I have photos but not on this computer - I'll see if I can find them.
With it being a wood wheel it's best to paint it with plastikote so it's wipe clean. The running surface is cork (nice for their feet) and you paint that too. I tend to just paint the inside of the wheel - never had a problem with the outside getting pee stained.
The plastikote comes in a little pot and costs about £4. Water based and safe for hamsters - virtually has no smell at all.
This is the plastic trixie wheel - doesn't attach to the bars though - I tried once and it fell off which wasn't very safe.
Trixie 61011 Rotating Ferris Wheel Hamsters, Plastic, o28 cm, Assortment: Random Colors : Amazon.co.uk: Pet Supplies
The wood one is silent however (has ball bearings). The plastic one is usually fairly quiet but not silent - some can be a bit rattly.