TJ, Actually you are incorrect regarding Reb Yaakov paskening it permissable to shake hands to avoid embarasement. In the mekor provided, Reb Yaakov states “Regarding returning a handshake to women when they extend their hand first in greeting, not in an affectionate manner, this is a very serious question and it is difficult to be lenient.” Reb Yaakov goes on to state that in a situation where there will cause embarasement, it requires further study whether it is permissable to be lenient or not. He never paskened one may be lenient in such a situation.
There is two prohibitions about this: 1) The Torah commanded to avoid all women with the status of nidah (Vayikra 18:19). and 2) It might lead to improper thoughts, which are prohibited (Kesuvos 46a; Shulhan Aruch, Even Haezer 23:3).
Reb Moshe, multiple times in the Igros Moshe, is very clear that it is assur:
1) EH I #56 page 144
“Concerning that which you saw people being lenient even those who are
yirei shamayim – to offer their hand to a woman when she stuck her hand
out. Perhaps they reasoned that this is not derech chibah and taavah –
but l’maaseh this is difficult to rely on.”
2) OC I 113 page 177
“To offer one’s hand to a woman in the manner of those greeting others
upon meeting. It is pashut that it is prohibited even for an unmarried
woman since they are niddah and surely it is prohibited for a married
woman”.
3) EH IV 32.9 page 76
“To offer one’s hand to a woman in the manner of those greeting others
upon meeting. It is definitely pashut that it is prohibited as I have
written OC I 113. That is because one needs to be concerned for the issue
of derech chibah and taavah. But I wrote in EH I #56…that one is to
dan l’kaf zechus those who are relying that it is not derech chibah and
taavah to shake hands. But there I wrote that l’maashe it is difficult
to rely on this. Furthermore I don’t see any inconsistency at all with
that which I permitted a person to travel on a bus because there –
there is basically no issue of chibah.”
Even if it causes embarassement it is assur according to Reb Moshe (see Halichos Bas Yisrael, vol. I, p. 110 n.33) and Nine to Five – A Guide to Modest Conduct for Today’s Workplace by Rav Shmuel Neiman, p.14 (“it has been rumored that Rabbi Moshe Feinstein, zt”l, ruled that it is permissible for men and women to shake hands. Nothing could be further from the truth! In his responsa, he agonized over this unacceptable practice and repeatedly stated that it is forbidden and infringes on giluy arayos”).
The Chazon Ish stated [re: a man shaking a woman’s hand who is not his spouse, his mother, his daughter, or his granddaughter] [p.p. 130-131])
A Yeshiva student from England refused to shake hands with his step-mother when greeting her. His father was extremely upset with his refusal. He demanded his son display “derech eretz” towards his step-mother and shake her hand. The son refused stating he was taught it was impermissable with a non close blood relative. This affected the fathers relationship with the son. Some family members told the son to give in al sholom bayis. The son asked a shaila from the Chazon Ish. The Chazon Ish responded with a short and sharp answer – “Chok V’lo Yaavor, Issur Gamur” (It is a prohibition that one dare not violate; It is absolutely forbidden,) Violating this halacha was out of the question despite sholom bayis and kibud av. (Oz Vehadar, p. 494).
Its also paskened assur in Responsa Be’er Moshe 4:130, and the Od Yosef Chai (by the Gaon Ben Ish Chai zt’l) Shoftim #22 where they rule it is totally assur. The Sefer Chassidim # 1090 writes one should not shake hands even if the person of the opposite gender is not Jewish.
Rav Shmuel Neiman, in Nine to Five: A Guide to Modest Conduct for Today’s Workplace writes regarding male-female interaction in the workplace:
It is forbidden to make small talk about matters unrelated to business. Men and women working together should not discuss politics, current events, recent tragedies or gossip, even if they do not do so regularly. Discussing these matters on a daily basis, is a violation of halachos that border on giluy arayos, which requires one to sacrifice his life rather than transgress. (p. 9)
When conversing with female employees or co-workers, one must be careful not to us the word “we,” so that the man and woman are not referred to as one unit. For example, one should not say, “We must talk with the editor,” or “We must purchase that software program.” Rather, he should say, “The editor must be consulted,” or “Please purchase that program.” (pp. 10-11)
It is a custom amongst yirei shomayim not to call a woman other than one’s wife or immediate family member by her first name, thus keeping a respectful distance between the two parties. Referring to a woman by her first name brings inappropriate familiarity into the relationship. Similarly, a woman should refrain from addressing a man other than her husband or immediate family member by his first name. (p. 20)
It is appropriate for male and female employees [to] refrain from all conversation when they meet anywhere outside of the office. This includes not discussing even job-related matters when meeting in the hallway or elevator at work.