you have your wooden disk, and your metal axle. I would try cutting a rectangle in the sides of the disk, not all the way through, and put a pin through the axle to hold the wheel on. you can do it on the inside too. it will look cool, and getting the second pin in will be a bit of a challenge, but it is guaranteed not to come out.
For the inner pin, use a small diameter steel bar, and for the outer pin, use some ultra stiff steel wire about the same diameter as the inner pin. bend the hell out of the wire, and it should spring back, into the gap you have. you can put tons of torque on this mechanism without it failing, and unlike glue, it cannot come apart if done correctly.
If you want extra reassurance, glue the pin into the rectangular slot. then you have the best of both worlds.