CIM Motor Direct Drive or Supporting Axle

[MrBasse]

The CIM shaft isn't that long to begin with, it will never make it through a wheel. A hub on both sides of the wheel would be the best way to do it without some extra engineering. I would look in to a wheel with some give to absorb the ball a little and grip it well. Since you seem to have found Andymark.com, take a look at their 8" pneumatic wheel.

Alternately you could do something like this. It would give you a reduction and would allow you to use a $5-10 wheel instead of a $40 wheel. The only downside is that the bearings in those wheels are horrific at any kind of speed over a walking pace when mounted on a cart (think terrifying vibration and 2nd degree burn heat [ask me how I know about the burns]).