All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We have already issued Fatwa 85264 on the ruling of a person who does not perform the prayer, so please refer to it.
Although your uncle does not perform the prayer, he is still your Mahram, so it is permissible for his female Mahaarim to shake hands with him or be in seclusion with him, unless this is not safe.
Allaah Knows best.