You are correct on the 6-32x3/8" size for the Button Head stainless steel cap screws. That is the size matches the original and I have been using replacements for many years after accidentally stripping the original.
I don't know how many "hardware" stores will have them. I found them most recently at "www.fastener-express.com". I believe they have a minimum order quantity of 100 like most everyone else but the cost wasn't much.