Moq, while I appreciate your arichus, nevertheless I do not believe you are correct in the Rambam. He clearly states that bfarhesia kanaimm pogin bo (and the Rayvad says that is only if he was warned). However, if it was btzina it is a gezeira mishum chasnus (that he might marry her). And if he does marry her, what is the issur? The answer is 4 issurei drabanan. True, the Rambam warns that one should not take this issur lightly, because there is no other issur where one’s children would be born non-Jewish. He quotes a pasuk in navi that one would get kares. But an onesh in navi can’t be on the deoraisa level. If it was, he should have said right away it is asur midoraisa.
Of course this is abhorent and nobody should think he has a heter to do such a thing. However, the point here is about Al tarbeh sicha, and then the discussion changed to shaking hands. If the root issur is drabanan, that is grounds to be meikil on the issurim which branch from there. Since it is not at all clear that shaking hands is derech chiba at all, any more than saying “How do you do, Maam”, there is certainly grounds to rule that it is a safek drabanan.
For a Jewish woman, the root issur is more severe, but still there must be derech chiba. Note that according to the Ramban, there is no deoraisa of lo sikrivu for the issurim which branch off, only for the actual mayseh itself. The rest of the issurim are medrabanan. Note further that this is why some amoraim would pick up the kallah and dance with her, because they knew there was no derech chiba for them on their madreiga.
As far as Reb Moshe, nobody here has yet managed to come up with the tshuva on shaking hands so we can all look it up. But what we do know for sure is that Reb Moshe was matir sitting next to a woman on a bus or train where there is also negia involved, because it is not derech chiba. Shaking hands in a business interview is simple manners and politeness. Is it derech chiba when you do it to a male interviewer (if you are male)? I sure hope not. So why is it derech chiba to a female interviewer?