benignuman – who wrote that most poskim allow shaking hands to avoid a so-called “loss of money”:
Chazal say that on Rosh HaShanah, it is decreed how much money you will earn in the coming year. Do you really think that your parnassa is dependent on whether or not you shake hands with someone of the opposite gender? Anyone who imagines that his parnassa is dependent on such factors is a kofer.
As far as a drowning woman – PUH-LEEZ. The halacha is that if a woman needs help (medical assistance, getting up after a fall, etc.), then it’s OK to touch her (to the extent necessary, and while being careful not to have inappropriate thoughts c”v).
Shaking hands with a woman is not medical assistance.