Rabbi Weitzman stated previously that there are Poskim who allow men to shake women’s hands if there is no sense of closeness or intimacy. However, I have read elsewhere there is no such Heter. As it is sometimes very difficult to avoid it, I would like to know where these Heterim are listed.

Shalom U'verachah, Thank you for raising this question. I have heard this from several Rabbis that I asked and seen it brought in books. Kol Tuv