This is certainly the way forward. Shipping to NZ is going to be expensive, and the chance of the prints arriving damaged is high. If the client claims that has happened someone is going to have to pay to get the print back here unless you are happy trusting them and just sending another one.
Get it printed there, and shipped direct to the customer. Then, if anything is wrong with it it can be returned to the print lab direct.
I originally agreed with printing abroad, however,
Depends a bit on quality control.
If it is printed here, then the OP has the chance to QA the item prior to shipping. If it is damaged in transit, a photograph of before and after would be enough to claim on the shipping insurance I would think (assuming you are going to insure it).
You then have to re-print, check and re-send, customer ends up with 1 good print, and one damaged print.
If it is printed abroad. You cannot QA the image prior to it getting to the customer. You are then let a bit sticky as to whether the colour etc. is correct.
Reprints/complaints have to be arranged on the phone, or via email, at a considerable time delay possibly.
Also, it feels like it reduces the 'worth' of the item.
It is no longer a piece of art that it being shipped, it is a photograph which is being emailed and printed.