Unless you already possess an appropriate visa for NZ, you'll also need a ticket out of NZ before you're let in. It doesn't have to be a return ticket, just a ticket to exit. In other words, you can't just turn up to NZ 'for an indefinite amount of time' without a resident visa.

I'm not too familiar with Skyteam, but perhaps you can back track slightly to China or Vietnam and fly from there?