All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Shaking hands between a man and a non-Mahram woman is prohibited. This ruling is not specific to the Prophet . Principally we are commanded to follow the Prophet, sallallaahu ‘alayhi wa sallam, in everything that is not proven to be specific to him. Allaah Almighty says (what means): {There has certainly been for you in the Messenger of Allaah an excellent pattern for anyone whose hope is in Allaah and the Last Day and [who] remembers Allaah often.} [Quran 33: 21]
Further evidence is that the Prophet explicitly forbade touching non-Mahram women, saying: "For one of you to be stabbed with a metal needle in his head is better for him than to touch a woman who is non-Mahram to him." [At-Tabarani. Al-Haythami, Al-Munthiri; Al-Albani: authentic]
Allaah Knows best.