Sorry for being frank and honest, I will say NO to this 十年無見的親戚. As you mentioned, if you have not been in contact with this relative for ten years, this means you are not at all close to him at all. Also, you are under no obligation to take him in. How can you allow someone to come to stay and intrude into your privacy...I cannot trust him.
Please just say no to him gently and hope he understands.