Reference: http://mufti.af.org.sa/ar/content/حكم-مصافحة-النساء
Question: He asks about the ruling regarding shaking hands with women, and whether it is prohibited, and whether shaking their hands nullifies the wudhoo?
Response: Firstly, it is not permissible to shake the hand of a woman who is permissible for him to marry, because the hand of the Prophet ﷺ never touched the hand of a woman. Also, touching a woman only nullifies the wudhoo if it [sexually] excites the desire where there is a fear that it might lead to the excretion of prostatic fluid – [the excretion of] which nullifies the wudhoo.
As for merely touching [a woman who is permissible for him to marry] without [sexual] desire, then this does not affect [the validity of the wudhoo]. [That said], there remains the issue of touching a woman [who is permissible for him to marry] – which is prohibited; so it is obligatory for him to refrain from doing that.