My father married a woman, but he divorced her before consummating the marriage with her. Is it permissible for me to visit her or shake hands with her?
Please note that she is his paternal cousin.
The woman with whom your father wrote a marriage contract but divorced before consummating the marriage is considered a permanent Mahram (unmarriageable relative) for you. This is according to Allah's saying,
And marry not women whom your fathers married, except what has already passed; indeed it was shameful and most hateful, and an evil way.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.