For what it's worth, I usually just clip them off with a pair of side cutters. I clip them down to just over the scalp. Have never had a problem doing it this way. Others may do things differently of course.
We had to disbud our 10 week-old buckling in July when one horn began to grow in again, weeks after disbudding him with a propane-heated disbudding iron. With the advice of a seasoned goat/sheep owner, we cut the one inch horn regrowth off with sharp nippers, quickly stopped the bleeding with blood stop powder, and then used wound spray. Next, we burned a ring around the cut with our new Reinhold electric tool and a buck tip, rolling it around in a circle leaving a black rim. Smokey had a little bit of a crying spell, but with ice, wound spray, and a nursing from his momma, he was fine right away.
Even though it was scary because of the blood, I am glad that we did this... a goat with one horn is dangerous (and looks strange!). The remainder of the old horn just fell off at the end of August.