You rightly said that I will answer that it was the adults fault. The bad act done with the weapon was giving it to a child, not the childs shooting someone. It gets clearer if the adult hands the weapon to a monkey or a randomized shooting machine. All three scenarios change nothing in regard to the moral responsibility of the adult.
I do not know whether the UN should ban nuclear weapons, but if someone uses a nuclear weapon and we would check out who might be morally responsible for the attack, I'd point at the attacker.
