Finding such music outside the Cook Islands and New Zealand is not easy, but one CD which seems to be widely available through usual internet outlets is "Drums, Songs and Chants of the Cook Islands". Recorded live in Avarua, Rarotonga in 1993, it features the Cook Islands National Arts Theatre.
It includes hauntingly beautiful chants from Raro, Pukapuka and Manihiki, and a drum dance from Aitutaki among its 13 tracks. I can recommend it because I have a copy myself which came from Raro Records (left) on the island. And anytime I want to be transported back to the islands - in spirit at least - I only need to put it on (Ode Record Company Ltd, Auckland, New Zealand - catalogue number CD MANU 1447)