one other factor worth noting: if you're going to have one brake, stick it on the front wheel, not the rear. that's where you have the majority of your braking power.
it's easy to lock up the rear wheel and make it skid (although I doubt your son has the hand strength for this). it's much harder to lock up the front wheel since it can't just skid being dragged behind the bike. people may worry about going over the handlebars, but in practice, this really is only a worry on a steep downhill with very impressive locking down on the brake - mainly for mountain bikers.
If you don't have experience working with this sort of problem, do it and have fun (but make sure to cover your bases), or take it to a local bike shop.