Options on converting away from the cotter pin cranks on bsa wayfarer bicycle
That's probably going to be an issue. Sheldon Brown has this page about BB standards:

https://www.sheldonbrown.com/cribsheet-bottombrackets.html

From that I'm guessing yours is probably 71mm x 1 3/8" X 26 tpi which is not going to be compatible with much of anything. I don't know if someone like Phil Wood makes cups to fit that size.