Island that isn't excessively humid?

You really can't have tropics without humidity. I would suggest the Cook Islands if you are looking for South Pacific. The climate is very similar to Hawaii.

The weather in the Cooks at the moment is actually quite pleasant - it probably averages about 24 - 27 C and the humidity is not too bad. Summer, however, is another story..

The west coast of Mexico November through April, Puerto Vallarta down to Zihuatanejo.

But surely there's somewhere in Oz that fits the bill it's such a huge place.

The Cooks are not humid from about May to September. July and August in particular might suit you, no need to turn on the A/C.

The winter months (July, Aug, Sept) are the least likely to be humid. We were in F.P. last Aug and it was not humid at all, The Cook Islands were unseasonaly cool in early Sept, Fiji and Vanuatu were very pleasant during Sept and New Caledonia was also unseasonally cool in late Sept. New Caledonia would be the most likely place to have the least humidity year round while still having the tropical ambience you might want - Ile de Pins in particular.

I second New Caledonia - the climate there felt almost more Mediterranean than tropical.
Very pleasant.

Tonga is also not humid in the winter, and I found Rarotonga cool even at the start of summer.

jmk - there are many many tropical places that are not humid. I have just been through an Indian summer of 42 degrees and 20% humidity.... give me 38 degrees and humidity any day!