I've heard that you risk ending up with an arrogant Basenji if you wait much longer than age three to neuter.
I have to laugh at that ! I have NEVER neutered a boy in all my years with the breed and despite having had 3 entire males with 5 pretty (and entire) ladies living with us as house pets at the same time.
Haven't had an arrogant male Basenji yet. The arrogant one is the pack Alpha - ME !
Maybe it is time for someone to reproduce Liz McCargo's excellent piece on why one should NOT neuter in most cases ?
But this boy is a rig. Only one descended testicle. THAT could indeed be a reason to neuter him, but on health grounds. Vigilance can keep him away from the girls.
But talk to your vet and find out the reason for this advice. Is the vet just saying it because it is in his DNA to neuter dogs, or does he think there could be a genuine health problem ?