nuclear weapons ⊆ WMDs; "nuclear weapons = WMDs" doesn't follow. (I was being sarcastic with the above comment; I don't actually expect MAFIAA to push for an US invasion into NZ - it's just the next logical upgrade from current situation)
NATO is the North Atlantic Treaty Organisation; New Zealand is in the South Pacific.
We haven't allowed any naval vessel carrying nuclear material (be it for weapons or power supply) to enter our waters since 1984. It's always been quite a point of contention with the US. It also happens to be a point of pride for the grand majority of Kiwis.
I'm guessing you aren't familiar with the current government. It's sad how weak the defense of New Zealand's position is now. Anything to grease the wheels of big money.