The tire should be a standard size one, the most common one that Jenny carries.
I wouldn't take the bobbin winder apart. 9 times out of 10 it's fine, but once I had one come apart in my hands, now I'm "spooked".
http://www.quiltingboard.com/vintage...e-t203282.html
At the end of the day the only thing that held it was super glue, and that wasn't permanent either. It's decorative only now. I wasn't able to find a 127/128 bobbin winder, only a 27/28 bobbin winder.