This may just be me, but neutering a goat is just cruel. If you don't want them breeding, don't put them together. Get anohter female and breed him with her. Goats that are "gelded" will still display certain characteristics that are normal for billies, but they're not as....peppy. They get sick easier.
Just thought I'd let you know. Anyway, good luck with your kid. Hope he's cute!