Training a cat that is literally painfully affectionate?

 
Training a cat that is literally painfully affectionate?
I had to take on someone else's cats. Though I am not used to cats, all three are easy to get along with. My problem is that one of them is endlessly affectionate, but does not seem to understand that claws hurt. He will climb up my leg while I am wearing shorts to get into my lap. He will climb my shirt to get to my face. Whenever he stretches, he digs his claws into whatever body part they land on.

I am told he is about 18 months old and neutered. All three cats wrestle and he strangely does not use claws when they do. He even gets along with my dogs. I am his only living scratching post. Can I train this behavior out of him without discouraging him from being affectionate in general?