Batman would never do anything to harm a child that age, no more than he would use a gun.
He saw his parents gunned down when he was a boy, and now he likes to see a boy that age take on armed men and win - to torture himself that he did nothing.
Interestingly while all the more recent constructions of Batman have him abhorring the use of firearms, a few of his first issues in the late 30s had him utilizing them for his own purposes.