Welcome to the forum. I have never had goats, but I did have sheep for many years. During those years, I never ever castrated a young male lamb. They were always sold after maturity for reproduction (breeding rams).
In my opinion, the sort of castration you describe is indeed cruel, painful and barbaric - especially without anaesthetic. A vet could do it for you, using a local anaesthetic. Otherwise, you can buy a special tool and some special bands. You can read about it here: http://www.wikihow.com/Band-a-Goat
Note well: even banding is a painful procedure and administration of lidocaine (a painkiller) is necessary. See note 2 of the notes above.
No animal should be subjected to unnecessary pain.