Chaos War Wolverine has a trait:
My question is, would he get the benefit of an opponent's modifiers to attack? For example, say the opponent has a hammer.

Yes he would. The opponent's combat value is calculated, 1 is added, and then it becomes a replacement for Wolverine.

From the RB
Modifiers apply to a character for as long as that character meets the modifier’s requirements, and are added up when needed to determine a combat value.