Oh please don't do that. I've seen a lot of mushroomed plungers, and I've never seen one so far gone that you couldn't simply file the mushrooming off, then dress the end of the plunger back into the proper shape and keep using it (with a tip on this time!). There's plenty of room to do the filing right in the cabinet, with the plunger held in place quite well, but if you'd prefer to use a grinding wheel or something, you can remove the entire assembly as one piece and get at the plunger end that way.

The plastic housings broke a lot, especially as the plastic aged. An old game that shipped with the plastic housing could easily have had a replacement metal one put on sometime in its life.