For the snapper: Preheat the oven to 400 degrees F.
Using a very sharp knife, score 3 deep slashes on each side of the snapper. Squeeze the lime juice all over the fish.
Stuff the prepared ginger-herb mixture into the slits as well as into the cavity of the snapper. Set the fish on a baking sheet lined with aluminum foil, and slide it into the preheated oven. Roast, uncovered, for 45 minutes, by which time the flesh closest to the bone of the thickest area should be perfectly white, and not at all glassy.
For the salsa: Meanwhile, use a potato peeler to make wafer-thin shavings of the coconut flesh. Mix the sugar with the lime juice, stirring until it dissolves, and toss with the coconut, and the lime zest, chiles, and cilantro leaves. Serve the salsa with the snapper