When should I neuter my kitten?

I'm 100% going to neuter my male kitten Arson since I have two unspayed females, one of them being his sister. I tried to make an appointment when he was around 4 months to get him spayed but they refused since he was so young. He was born at least 2 weeks before August 22nd. I don't want to risk any inbred babies with his sister (I don't care that most cats are inbred, it just doesn't feel right). So when would the best time be to neuter him? I want to do it as soon as possible. He's around 5 months now I think, but I don't know his exact age because I found him when he was around 2 weeks old.