dear noitallmr…..First, mussar seforim are not halacha…also, Ii have no idea why there should be any discussion about shaking hands in mussar seforim…
Second, you mentioned the mishne berurah…OK, please can you quote where he discusses shaking hands with another gender?
Thirdly, there is a difference beteeen men and women on that. For example, is listening to the voice of a man “ossur’ for a woman? NO- because the lav of “loi sikroivu’ has a limited purpose.
Lastly, I will bring you some mekoros that fully allow shaking hands because it is not derech chibah.
Again, I did not say that everyone holds by this but there are enough Poskim of great stature who do hold that shaking hands is not ‘begeder chibah”.