Preheat oven to 325°. Use an ice pick or screwdriver and a hammer to pierce the eyes of the coconut. Set coconut, eyes down, in a colander set into a bowl to drain (the coconut's milk is great to sip). Place coconut in oven on a baking sheet and bake until cracked around center, about 25 minutes.
Let coconut cool slightly; then, using the claw side of the hammer, tap the coconut all over to break into chunks. Pull off and discard shell, and then pare brown skin from coconut flesh. Cut flesh into large chunks.
Arrange coconut, mango, papaya, pineapple, and limes on a large platter. Combine salt and cayenne in a small bowl and serve alongside fruit for dipping.