Leave the radio at home
We've all seen the advertisements in the back of QST, but there are resources on the web, too. One such site is DX Holiday. Some of the information is out-of-date, but overall it is an excellent place to begin looking for some options. Here are just a few:
There are also places where you can bring your own radio but the antennas are already set-up such as this one in the Bahamas.
As you might expect, rates vary by season and some big contesting weekends might be more expensive than "regular" weekends. The seasonal rate change might actually work in your favor, though. Consider most people do not want to go to the Caribbean during hurricane season, though CQ WW SSB falls at the very end of that season (the last weekend in October). If you can reserve some station in the Caribbean, you may be able to get flights for a deep discount!
Traveling light, or with no equipment at all, is not cheating. When I give my 100 Pound DXpedition talks, I state up-front that the way I categorize DXpeditions is by the volume and mass of stuff that is taken. Hauling zero equipment is the first category I discuss!
If you're not sure if this kind of thing (DXpeditioning) is for you, perhaps renting one of these places with equipment already there is a good first step. That would let you "try before you buy". Of course if you do try this, please drop me a line and let me know how you liked it!