Sure Wolverine has healing powers & adimantium claws, anyone who percept heroes on powers alone are those who only look at the exterior part of heroes.
Batman is more than batterangs, batmobile, & batsignal; he is more than that. Batman is obsess, that he would do anything to accomplish his goals, but he would never resort to murder. He was fought superhumans, demigods, & even gods themselves despite having no super powers. And time & time again, he triumps over all of them.
Right there! And i be damn, Magneto whipped Logan's ass good and a Sentinel once killed future Wolverine. I have all my faith that Batman would go and investigate more of Wolverines background and nail him flat, hell Batman even beat Superman for crying out loud!
besides, he DOES use guns, he ALWAYS "COINCIDENTALLY" has that gun that he uses to cling on buildings. funny that it's relatively large to be in his utility belt, yet when he falls of a high place he always has it.