feivel, I’m glad there was a happy outcome to the story. May your brother have a full refuah quickly!
I was told by my Rav that a prominent, well known Rav (who I won’t name for obvious reasons) shakes hands with a non-Jewish woman once per year.
There are questions regarding if a non-Jew makes a kinyan in the same way as a Jew. One opinion is that when someone sells something to a non-Jew, the kinyan is made with the normal way of “sealing the deal” in society.
This Rav sells chametz before Pesach for a large number of people, and he sells it to a woman. He is careful to use a few different forms of a kinyan to satisfy all opinions, so that the sale and transfer of ownership is valid. Since it is normal to shake hands to seal a deal, he will shake the woman’s hand to transfer ownership of the chametz to her.