ちょうど先日似たような質問をPassport Centreにしたところでしたので、
もらった回答をお伝えしますね。

太字の部分がお役に立つかと思います。
Witness探し、大変ですよね…私はなんとかこちらで見つけることができたので
Statutory Declarationを作成といった面倒なことにはなりませんでしたが、
国外からだとこれすら難しいかもしれませんね。

無事に申請が完了しますように！

The witness must:

· Hold a valid New Zealand Passport
· Have known the applicant for at least one year or since birth
· Be aged 16 years or older
· Not be related to the applicant
· Not be your spouse or partner
· Not live at the same address as the applicant

If you do not know anyone in your current location who meets the witness criteria you will need to send your application to someone, perhaps back in New Zealand, who meets the witness criteria and have them complete the witness section.

If you have exhausted all avenues in trying to locate a witness to no avail, you will need to complete a detailed Statutory Declaration and submit this with your application for the Passport Office's consideration.

The Statutory Declaration will need to state that you cannot find a suitable witness, the reasons why, and the attempts that you have made to locate a witness

The witness section will need to be completed by one of the following professional groups:
· Lawyer
· Police officer
· Applicant’s employer
· Teacher
· Kaumatua
· Minister of religion
· Registered medical professional.
Additionally, they must write the full name of the person applying for the passport on the back of one of the photos, and date and sign their own name on the back of the same photo

Please note, we cannot guarantee that the Statutory Declaration will be accepted in lieu of a suitable witness.