The proposed setup ("UN member states" , "Associated states of New Zealand", "Other territories") is one I also considered. The reasons for rejecting it are MOS:LIST and aesthetics. The proposed categorization is not very tidy; it looks as if we had a list divided into: "Stars in the Milky Way", "Stars around planet X in another galaxy" and "Other stars". Lists should strive to have as few categories as possible (while retaining as many as are necessary for meaningful distinctions) and a single main criterion for dividing them (in this case, stand-alone sovereignty could work as the main criterion and UN membership as a secondary one). Categories should be made to encompass several items with similar characteristics, not be custom-created with one or two items in mind. 
(Not directly related to the organizing criteria, but must be noted) It must also be noted that in the specific Oceanian case, full membership of CI and Niue in the Pacific Islands Forum is also a marker of sovereignty among the states in the region, and must be emphasized as much as other aspects.