- R. Yosef Tzvi Rimon (Tzava Ka-Halakhah, pp. 318-323) discusses whether a male soldier may shake the hand of a woman soldier (or vice versa). He goes through the sources and concludes that it is a debate whether it is permissible and therefore you shouldn’t initiate the handshake and if she initiates it you should to elegantly refuse. But if that isn’t possible then you may return the handshake.
However, he writes that when you meet a woman on an ongoing basis you should explain to her once that you don’t shake hands. Also, and this is significant, army and educational (i.e. college) settings require great caution in intergender relations and therefore you should be strict on this issue.
- In this lecture (link, starting at 5:45), R. Hershel Schachter quotes a responsum from R. Chaim Berlin permitting shaking hands with women.