I asked my Rav years ago about shaking a woman’s hand in a business situation. His answer was that I shouldn’t extend my hand first, but if she did I should shake it. As usual, those of you who are shouting “assur assur assur” are assuming everything is black and white, with no shades of gray.
(BTW, one of the advantages I’ve noticed here in Israel is that women here who are obviously not dati usually don’t shake my hand, nor do they expect me to shake hands with them. It takes some getting used to, but add that to the reasons to make aliyah.)