I have a machine with a short shank that has snap on feet. The walking foot does not snap on though. I have to unscrew the "ankle" and screw on the walking foot.
Do you have a local quilt shop? If so, I'd ask if they have a generic walking foot you can try.
If you want a decent, low priced machine that you can readily get parts for, try a Kenmore. I bought them for my daughter's in law at Christmas for less than $100. They're not bad for a basic machine.