If you go one way you will lose a day of your trip, conversely, going the other way you get a day longer. something to do with the international date line !
whaaaat ?
the Cook Islands are lovely but not cheap to get to (out of Auckland is about the only way, I think), so consider whether you have to go there. If you're flying out of the UK, Thailand or Singapore are probably the cheapest flights and the best hubs for visiting other Asian countries; and it may be simpler to go to Oz before NZ. Try Trailfinders, they're very good at arranging this sort of thing.