Fablon is basically patterned stick back plastic, we use it on wood to make the wood easier to clean and protects the wood from water getting to it. The only reason I don't want it on the running surface is because when it can be a bit more slippery than plastic, and so I dont want to put on the area she is running on.
Maybe try searching patterned sticky back plastic ??
From looking contact paper seems more like paper that has a stick back, which isnt the same thing.
I'll probably be making my wheel on either the 15th or 16th or 19th June, depending when it gets here and what time I have. I'm happy to show you a picture when its done.