You're much better off bringing your film with you, in your carry on baggage. A few passes (or more) will not harm it. (When living & working in Europe, I used to always pack a little Minox 35GT, usually loaded with ISO400 colour neg. Sometime that camera would have done 10 or more return trips with the same film loaded, and I never experienced any x-ray damage).
Make sure you declare anything and everything, especially for the quarantine declaration.
As mentioned, get some decent, high SPF sunscreen. Oh, and insect repellant for the South Island.
(BTW, technically it is illegal to kill sandflies when you are in a National Park )
So, how long do you have? The length of time you have will largely dictate your route.
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