I was incorrect in stating R. Yisroel Belsky’s view on the subject. This is what someone involved in kosher supervision, in a position to know R. Belsky’s view, wrote to me:
Rav Belsky holds that, generally, a mashgiach should NOT shake the hand of a female factory official. He holds that the Hetter should be used ONLY in isolated incidents–and when accompanied by personal protective acts to restore the level of pre-deviation zehirus and to maintain kedushah.
Also, Toby (Bulman) Katz wrote of her father’s (R. Nachman Bulman) position:
My father zt’l permitted shaking hands if the woman extended her hand, to avoid embarrassing her. A man should not put out his hand first.
I see that R. Zvi Lampel relates his personal experience with R. Reuven Feinstein:
I asked R’ Reuvain Feinstein, shlita, and he insisted that Rav Moshe permitted handshaking with a woman where she extends her hand first, on the basis of avoiding the issur of embarrassing her.