This is the weapon of the enemy.
Well, except for the original version of Batman, who had no problem blowing away people with guns.
And Burton’s Batman, who tried to strafe the Joker, and used bombs to blow up an occupied factory.
And Nolan’s Batman, who arms the Batmobile, Batpod, and Batwing with lethal machine guns and other projectile weapons which he uses in a crowded shopping mall, and at one point narrowly avoids blowing up a car with two kids inside. On several occasions in the Nolanverse, in times of extreme need, he has no way of being sure his gunfire won’t kill someone. Alfred even calls him out on how lucky he was not to kill someone in Begins.
In fact, even the version of Batman depicted, from The Dark Knight Returns, uses a rifle to fire a grappling hook, and the Batmobile’s main cannon is perfectly lethal, though he never uses it. The secondary weapons are rubber bullets firing from machine guns, which could only be consistently non-lethal by comic-book physics.
So, yes, aside from all those times Batman uses guns, Batman doesn’t use guns.