You live in a perfect place for many species of chameleons! I used to live on St. Croix in the US Virgin Islands. Does Curacao allow chameleons to be imported? I know there are a lot of restrictions and bans of things like chameleons in the US Virgin Islands, Puerto Rico and of course Hawaii. Being such a small island in the Caribbean you won't have too much heat to deal with but I don't think it will be cool enough for most montane species which really need a lower temperatures, especially at night.
Look very carefully at your maximum temps both day and night during the dry and rainy seasons. Then look at the climate of where the chameleon you choose comes from.
What species are you planning on getting? I think a panther would be in heaven although I know very little about panthers.
I would not place the cage in direct sunlight, but in a place where it will get dappled light and there is dappled light all around the cage. Chameleons live in the forests, which are much cooler than the same area that is open and covered only with shrubs. I would place the cage where the ground is quite shaded so the sun baking on the ground doesn't heat up the air around the cage. It is quite surprising the difference in temperature between under the canopy of a rain forest and a field 100 meters away. I have a veiled chameleon, a supposed heat lover, outside and he will blanch from heat stress if the area around his cage receives full sun. He basks in the morning and afternoon and hides during the mid day.
I'm looking forward to seeing pictures of your cage, finished or not. Please tag me in any of your posts about your cage, etc. I do miss the Caribbean where I spent over 8 wonderful years. After eleven years in Saudi Arabia followed by eight years in St. Croix, I just cannot get used to the cold even though I've been in south central Texas for four years--even though I grew up in The Great White North of Canada.