Can't help with the export part from NZ., but here is a little something to make it even easier to get in the U.S. Just cut and paste and include it with shipping documents presented to U.S. Cusotms

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To Inspectors of the Bureau of Customs and Border Protection,

The enclosed firearm/part was manufactured in or prior to 1898 and meets the definition of an antique firearm under Title 18 Chapter 44 section 921 (a) (16) of the Gun Control Act of 1968. For the purposes of importation under Part 47, this firearm is defined as “not a firearm” in Subpart B section 47.11. Part 178 Subpart G 178.115 makes the importation of this firearm an exempt importation. No import license is required.

This firearm is being imported for personal use and is not for resale. This firearm is exempt from duties as an Antique under HTS 9706.0000.60.