Most of the Vans 'classics' models seem to come in size 16, as well as Converse Chuck Taylors. Outside of that, size 16 pretty much rules out all 'skate specific' shoes that I'm aware of, but you can look for skateable shoes from the big sports brands' non-skate/casual lines. You're basically just looking for a flat rubber sole and a durable upper (mostly suede or leather). My search for skateable shoes that come in size 16 yielded the Adidas Pro Model, Air Jordan 1, Nike Air Force 1 (a little clunky for skating, but they'll work), Nike SB Janoski and Janoski slip on (these seem to only be available in big sizes through custom order). I tried the Asics, New Balance, and Puma sites, but couldn't find anything skateable that comes in a 16.
I know shipping to NZ can be prohibitive to buy from other countries. If you can't find anything on those brands' local sites, I would check with a sporting goods store - they may be able to order them from the company for you.
I don't know if NZ has Marshalls or an equivalent discount store, but that might be worth a look - they often have shoes in big sizes, and they're usually at a huge discount due to the size.