. You just need two round flat washers. There are already two screws in the bottom of the base that screw into the stand. You take the base off the wheel (it used to just pull off but my last one was glued on tight and had to be partly sawed off, but it came off cleanly). You then use the screws and washers to screw into the existing holes in the stand (base removed) with the wheel and stand upside down in the cage. The washers are on the outside with the screws going through into the stand. It was very stable when I did it. It means there is a bit of substrate under the wheel but still not a huge amount.
Are you in the US? (I know you can still get wodent wheels there). 11" wodent wheel attached to the top works well. It's the best size wheel to fit in that cage. I have a photo comparison somewhere = I'll see if I can dig it out. It's the most compact 11" wheel and I actually think it's safer hung upside down (I just used two cable ties in strategic places to secure the stand to the top bars).