Praise be to Allah.
It is not permissible for a man to shake hands with his wife’s sister or aunt, and it is not permissible for him to be alone with any of them, because they are not his mahrams. Rather marriage to them is temporarily forbidden, but this is not enough to make them like mahrams with regard to being alone and shaking hands with them.
If it is established that a person is a mahram through blood ties, breastfeeding or ties of marriage, then that is permanent. There is no such thing as a temporary mahram, rather there is a temporary prohibition on marriage. The wife’s sister or aunt are not mahrams of a man, rather it is haraam for him to marry any of them whilst he is still married to his wife, because Allaah says (interpretation of the meaning):
“Forbidden to you (for marriage) are: your mothers, … and two sisters in wedlock at the same time”
And because the Prophet (peace and blessings of Allaah be upon him) forbade being married to a woman and her aunt at the same time. With regard to the wife of another man, she is temporarily forbidden to anyone other than her husband, so long as she is still married to him. If the marriage ends through his death or through divorce or annulment of the marriage contract, then it becomes permissible for someone else to marry her after her ‘iddah ends, even if he already has a wife, so long as she is not a sister or aunt of the first wife.
And Allaah is the Source of strength.