I think that it’s going to be a tough sell to the Kiwis. Until 12 years ago, New Zealand didn’t even allow US nuclear-powered warships in her waters, because there was that much concern from the Kiwi public about them.

https://en.wikipedia.org/wiki/ANZUS

New Zealand was suspended from ANZUS in 1986 as it initiated a nuclear-free zone in its territorial waters; in late 2012, New Zealand lifted a ban on visits by United States warships leading to a thawing in tensions. New Zealand maintains a nuclear-free zone as part of its foreign policy and is partially suspended from ANZUS, as the United States maintains an ambiguous policy whether or not the warships carry nuclear weapons and operates numerous nuclear-powered aircraft carriers and submarines; however New Zealand resumed key areas of the ANZUS treaty in 2007.[3][4]

ANZUS was overshadowed in late 2021 by AUKUS, a trilateral security pact between Australia, the United Kingdom, and the United States. It involves cooperation in nuclear submarines that New Zealand will not support. Australia and New Zealand, "are poles apart in terms of the way they see the world…I think this alliance underlines that they’re going in very different directions,” said Geoffrey Miller, an international analyst at the Democracy Project in New Zealand.[5]

AUKUS is specifically about submarine tech, not just tolerating someone else’s subs passage. The Aussie government may have wanted nuclear vessels and decided that the public was finally sufficiently on-board, but New Zealand has had more opposition than Australia has.