But help you I shall, just to show what a big heart I have. Plus I'm paid to do it (editor's note: overpaid, we're starting to think).
What you need is some sort of inflatable kayak, which will pack down fairly compactly yet be seaworthy enough to get you from side A to side B of your little tropical isle. At the high end, price-wise, you have the Innova Safari, an excellent inflatable with the less-excellent price of $600 (www.innovakayak.com). But, it's a sturdy unit, with overall performance not that far from a rotomolded boat. The makers report it can handle up to Class III whitewater, ocean surf, and even eskimo rolls. It weighs 24 pounds, and packs down to about 20 by 17 by 10 inches. Or, about the size of a suitcase. Legit carry-on luggage, in other words.
At the low end of the price parade, you'll find the Sevylor Tahiti ($200; www.sevylor.com), which is made of PVC as opposed to the rubber and polyester material of the Innova boats. Weight and packed size is about the same; but the Tahiti is really a calm-water boat and is best suited for dunking around in lakes. Still, on gentle seas, close to shore, I don't see any reason why it won't do the job for you.
And pack sunscreen!
More kayak reviews and advice in Outside's 2004 Buyer's Guide.