Possibly but I've already got the uhmw in the car. It has to be food safe. HDPE would have worked but isn't recommended for low temp applications so a slushy machine would be a problem. Delrin is foodsafe but can release chemicals at higher temps and the machines are cleaned with hot water. I think the original part is uhmw so we're going with that.Rig a vacuum nozzle to suck away the swarf as it forms; however, don't try to suck up a load or you'll end up needing to clear a ball out of the hose!
Can you use Acetal (Delrin)? still a pain but less so than UHMW.