I don't want to help my father do certain mechanical work
The question is, do you find mechanical work difficult? Or is it just unpleasant to work with your father?
I don't like working with my hands
You are entitled to work how you want to. You should however still help your father, he expects it. He might be very angry at you if you don't and not talk to you anymore.
But what if I took this as an opportunity and told him I don't care about him.
I think he might feel very hurt if you refuse to help him and tell him off. You should have some respect, he has made a lot of sacrifices for you it is only fair to help him back.