Mayan_Davash,
You wrote, “You’re probably referring to cases of Ones (one is essentially forced to do so). In my professional career, I was always able to avoid shaking womens hands in a cordial manner. So why would shaking a non-Jewish female’s hand not be 100% assur?”
Are you saying that because you were always able to avoid shaking hands with a non-Jewish woman in your career, no other Jewish man is permitted to shake hands in a business setting with a non-Jewish woman? Or are you just saying it would be assur for you to do it?