All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is prohibited for the Muslim woman to shake hands with non-mahram men. The evidence on this is that Mu'qal Ibn Yasar, may Allah be pleased with him, narrated that the Prophet [peace and blessings be upon him] said: "It is better that you be struck on your head with an iron needle than to touch a woman you are not allowed to" [Al-Tabarani in Al-Mu'jam Al-Kabir, vol.20 pp.211].
Ibn Hajar, in addition to Al-Monthiri and Al-Haithami said that its Isnad is sahih. Moreover, the Prophet (PBUH) used to say: "I don`t shake hands with women." [An-Nasa`i].
Moreover, Al-Hafid Al-Iraqi (May Allah have mercy on him) said: "Our fellow scholars (Shafie) and others said: "It is prohibited for a man to touch any part of the non-mahram woman, such as the face. However, they have disagreed about the permissibility of looking at her face when there is no arousal of sexual desire. The prohibition of shaking hands with a non-mahram woman is greater than looking at her in case there was no necessity for that. However, in case of necessity, such as treatment, it is permissible that a male doctor treats her."
Non-mahram men refers to all the men who are lawful for the woman to marry including those temporarily forbidden in marriage (sister`s husband, paternal aunt`s husband, and maternal aunts husband).
Thus, it is forbidden for her to shake hands with the latter. And Allah the Almighty Knows Best.