@pedro47, in my experience, the shoulder seasons are "generally" less crowded, as others have already said. We always liked traveling to Hawaii during the middle two weeks of May. Weather was great, never too hot, Winter rains had calmed down, kids weren't yet out of school, and all in - it was a great time to visit Hawaii. Best of all, going in May, things are lush and green. If you go in the Fall, a lot of landscapes are sunburnt and dried. So we like Spring better. That said, late September into October is also pretty good on most islands, as long as you plan ahead. We aren't "lay on the beach" people, so if the weather is cooler, or even a bit cloudy, it makes for a more interesting visit.
But there is a balance to be had. If you're visiting or staying on the rainy side of an island, you may want to go during a higher season, to have less rain. Unless it's Kauai, where the trick is to go north if it's raining down south, or south when it's raining up north. On an island like Oahu, where the Koolaus divide things into "windward and leeward," sides, so "wetter and drier" sides, you can alternate which side of the island to spend your time, to minimize the rain. But then, there are times where a good Hawaiian rainstorm can be invigorating. (Going to the Pali Lookout on Oahu on a windy, stormy day can be exhilarating.)
At the end of the day, if you're doing a timeshare exchange to get there. you may be limited by the availability of the timeshare you're offered. Then the quality of your trip boils down to where you will be staying, and what you expect you might want to do with your time.
You being military - are you eligible to book the Hale Koa in Waikiki? If so, pursue that. I've stayed there numerous times, and it was really nice - for what it is. It made a great jumping off point for things to do on Oahu, and a great beginning or ending point for a two-island vacation.
Lots of options, and no one right answer.
Shoot me a note if you want other ideas.
Dave