Yosi7:
Rav Dovid Feinstein has said on many occasions that Rav Moshe held handshaking was muttar but didn’t write in a teshuva because he didnt want to be attacked for another Kula. (he was already attacked for many others).
I’m going to have to see a source for that before I even consider believing it. R’ Moshe was known for stating what he believed to be the truth regardless of what other people might think of his position or of him personally.