jonnyp, Not sure where you are leaving from. I looked into this when I was in Sydney about five years ago after deciding to ride half of Australia to get to Sydney and then get a boat to NZ. I wanted to keep off air flight the best I could. But my dilemma was in ability to handle sailing on a small boat which seemed to be the only available option in terms of affordability and availability. I was told that you might be able to help crew on a private yacht (although I have little skill in the area) and I the thought of death from sea sickness was not appealing or I didn't have the bottle.
I tried the freighting companies by phone to get a lift on a frieght ship but they didn't seem willing to let me jump aboard. However I approached them through the front desk operation, maybe if I'd pedalled down to the dockyards the captain of the ship would have agreed.
The cruiser option was way too expensive. In the end it was air flight unfortunately. But if you have a good stomach maybe a hitch with a private yacht travelling through might still be a winner for you.
Enjoy NZ, the cycling was brilliant and the rest was just as good. PS take wlkaing boots too, the walks are magic.