Not sure about NZ, but in 2008 I sent my bike by air from Indonesia to Australia using a wooden crate. Once complete, the crate had to be taken to a special fumigation treatment, that took 24hrs, and I got a certificate of this for the Oz quarantine inspection. Of course this was 4,5 years ago, so maybe wood material is not allowed any more. Their government webpages should know, how it is (google: biosecurity new zealand).
Or, you could try to contact some motorcycle dealers, and ask if they could find you a factory crate. Those are usually made of metal.
I would think NZ, like Australia, demands all vehicles be "clean as new", when they arrive, and this means no ordinary washing, but really making sure, that there is no earth material or any dirt, anywhere. I've heard of vehicles completely rejected entry to Oz because they weren't properly cleaned.