I think it will be less about hunting but more about dealing with and surviving actual wilderness (I presume your hunting trip will be relatively adventurous, cause otherwise why bother?)
Doc website, topo maps and the legal requirements are a must. Not sure what the regulations with regards to firearms for non-residents are nowadays, and how you plan on tackling that.
There are plenty of clips about hunting in NZ in Youtube. "South Island riflewalkers" and "kiwi bushman" are entertaining "keeping it wild" is a bit more realistic. Will give you an idea what to expect.
Also put in some practice/exercise... Can you hike through difficult terrain/bushwhack for 8 hours with a 30+ kg backpack?
Honestly for a "once a lifetime" trip i would likely head over to the west coast or fjordland and book a helicopter trip. Heli operators normally know the good locations...
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