Praise be to Allah.
It is not permissible for a man to touch in greeting the hand of a woman who is not his mahram, even if she covers her hand with her garment, because of the hadeeth narrated by al-Bukhaari in his Saheeh from ‘Urwah, from ‘Aa’ishah (may Allaah be pleased with her), in which she told the story of how the women gave their bay’ah (oath of allegiance) to the Messenger of Allaah (peace and blessings of Allaah be upon him). She said: “No, by Allaah, his hand never touched the hand of any woman when accepting the oath of allegiance, all he said was, ‘I accept your oath of allegiance on this basis.’”
And Ahmad narrated with a saheeh isnaad from Umaymah bint Raqeeqah that she said: “I came to the Messenger of Allaah (S) with other women to give the oath of allegiance to him, and he accepted our pledge to abide by what is in the Qur’aan… We said: ‘O Messenger of Allaah, will you not shake hands with us?’ He said, ‘I do not shake hands with women. Rather what I say to a hundred woman is what I would say to one woman.’”
And we have in the Prophet (peace and blessings of Allaah be upon him) the best example. The One Who sent him said (interpretation of the meaning):
“Indeed in the Messenger of Allaah (Muhammad) you have a good example to follow for him who hopes for (the Meeting with) Allaah and the Last Day, and remembers Allaah much”
And Allaah is the source of strength.