The pump only consists of the metal cover, the gasket, and the plastic diaphragm. If the gasket looks to be in good condition, I would just replace the diaphragm, but I’ve had some trouble with a fuel pump not sealing recently, so that might just be my personal experience speaking.
Your pulse nipple should be fine. Mine came that way when I ordered a new set of carbs. It was damaged in shipping, and isn’t something that breaks very often while installed in the ski.