I think you'll find that it's a bit more complicated than that, Sbt
The TTMRA is about occupations, not private recreational activities. My recollection is that for non-IFR private pilots you have to apply to the NZ CAA and do a check flight and test with a recognised CAA examiner. There are some differences, such as the NZ version of the hemispherical rule slices the sphere East/West rather than North/South. But it shouldn't be too hard. Have a look at the NZ CAA website - that's where I found the info when I was planning a jolly across 'the dutch'.
As KL notes, finding someone who'll hire you an aircraft to fly into Milford Sound is a very different question. They have real mountains in NZ.