Shaking a Woman's Hand

Question: In the text message responsa from last week, on the question: If a secular woman puts out her hand, can I shake it? Ha-Rav answered: No. Politely apologize: Forgive me, this is saved for my wife. I once heard that Rav Moshe Feinstein when facing the same situation would shake her hand. The reasoning being that not shaking a woman's hand is a Rabbinic prohibition but embarrassing a person is a Torah prohibition. Was this in fact the case and if not, what about applying the above reasoning and allowing the handshake?
Answer: Rav Feinstein did mention this idea in his Teshuvot (Igrot Moshe, Even Ha-Ezer 1:56) but concluded that it is difficult to rely on it. The Beit Yosef (Yoreh Deah 195) mentioned that according to the Rambam it is a Torah prohibition and one should be killed rather than transgress it! We should not embarrass anyone, but here she is causing herself embarrassment. Ha-Rav Ovadia Yosef declined to shake hands with Prime Minister Golda Meir when he received the Israel Prize. And Rav Mordechai Eliyahu did not shake hands with the Queen of England. In both cases, apologies were issued to the Rabbis that very night for putting them in that situation.