That sounds like a good idea Shannon. You'd need to unscrew the wood base to do that and then it would depend on the depth of the back piece the wheel is attached to - I have a feeling it would be too deep to fit through 1cm bar spacing.
I used to have ours directly on the base of the cage, a little bit of substrate around it and then slope the substrate away from it so it got deeper and deeper the further away from the wheel it got. It seemed to work ok. I'd worry about a hamster trying to dig underneath it if it was on top of the substrate.
Another option would be to have the wheel sat on a low platform and tie the back strut to the bars with some sisal string to keep it stable. Rodipet actually made a wheel platform that is 9cm high. It has a cut out to fit their wheels but I reckon the stand of the Karlie wheel would sit fine in the cut out bit. It depends on height then - the Karlie wheel is 32cm tall I think. Plus 9cm stand would make 41cm tall - which would fit in a Barney - but you'd need minimum 42cm internal height in the cage.
Here's the rodipet platform, or you could maybe make something similar. I like the idea of their platforms as it means the hamster can go under the wheel safely and use that area of substrate, and the wheel is stable - I do think you'd need to steady the wheel on a platform though, by tying the back strut to the bars so it couldn't fall over.
This one is designed for the wodent wheel, but if you took the wood clip bit off the top it would be a virtually flat platform (just ignore the grooves).
https://www.rodipet.de/shop/laufraed...ent-wheel.html
Or this one is the one with the cut out area for their wheel base - you'd need the larger one linked so the Karlie wheel base would fit. Or you could fill in the cut out with something - cardboard or something, to make it flat
https://www.rodipet.de/shop/laufraed...rklaufrad.html
I'd been thinking of doing something like that - I'd like the one for the Wobust wheel.