I think you could probably see nuclear depth charges and nuclear tipped interceptor missiles used without necessarily provoking a nuclear response. More specifically, I think that in those applications the fact that the weapon used was nuclear doesn't inherently escalate the situation any more than using conventional weapons - it just increases the likelihood of destroying an enemy asset and killing enemy personnel. The real danger is that two nuclear armed powers are in a position where they're dropping depth charges and intercepting missiles in the first place.
Personally, I think it is important that both of those applications are somewhat "peripheral" in that while using nuclear weapons is more effective, it isn't an absolute game changer in the way that other strategic and tactical weapons are. A nuclear depth charge gives you the near certainty of destroying the submarine in question, and a nuclear interceptor gives you better odds of taking down the missiles you're trying to intercept but neither is on the same level as destroying an entire city or army with a single bomb. It's also worth noting that both of those are applications were nuclear weapons have been phased out and replaced with guided munitions because they offer similar benefits in terms of a greater likelihood of destroying the target. Basically, applications where the action itself wouldn't initiate WWIII are the ones where using nuclear weapons wouldn't do the same.
For potential scenarios, maybe an India-Pakistan dust up or something between North Korea and the South/Japan/US where one of the parties uses a nuke without escalating the conflict. But I can't see anything between the major nuclear states that doesn't escalate.