Batman would fight wolverine once. Wolverine would know who batman was under the cowl because of his keen sense of smell, wolverine would pop his metal claws, wolverine would heal, and wolverine would show some skill in martial arts. Batman would notice all of these things. Batman would find some way to escape.
Next time they fight, Immediately military grade gas grenades will be utilized to throw off wolverine’s hyper senses. High voltage tazer would come into play. The metal that laces wolverine’s bones would act as a conductor, frying wolverine. OH batman figured that wolverine’s bones aren’t osseous because as they fought the first time wolverine is far heavier then his 5’3 frame would allow. The metal claws popping a sheath would wear out bone overtime so he assumes that if the forearm sheaths are metal so is the rest of his framework. If wolverine wasnt incapacitated from the violent electroshock, wolverine most likely would be pissed.
So as wolverine is thrashing about from the disorientation of the shock, and the gases. (Not utilizing all those years of material training because he falls to a bzerker rage) batman tosses some sort of sticky material at wolverines face. The material permeates over wolverine’s head tenaciously until it cuts off his breathing supply. Wolverine is done and batman has some nasty booboos