Why does Johnny decide to let Dr. Warren fix his hand?

Johnny allows Doc Warren to operate on his hand because he will regain some use of it, even if he never gains full use. Warren tells him he may still not be able to go back to his work as a silversmith, but Johnny only wants to know one thing.... if he can hold a gun. He agrees to the operation.

He wants to be able to use his hand again, even if it will not be usable to the full extent. Also, the pride that kept him from saying it before is now gone...he is more humble and less self-conscious.