The common understanding is that 'no 1931's' [ with the 3 piece rad. shell] came to New Zealand.
The Canadian shipment records do not list cars sent to NZ, but some did arrive here.
I believe the few that are here came as one off dealer orders, and speaking of Bick, his coupe is a 1931 with the roll down back window & was sold new in early 1932. There is also a 1931 Tudor not far from where I now live & it has always been in this area from new. There are about 6 NZ '31's I know of, but Bick is the authority onh Model A's in NZ.
Of course, quite a few imports of '31's has occured in recent years, but the interesting ones are RHD from Argentina.