Remove wide strips of zest from one of the limes, using a vegetable peeler. Combine with the sugar and 3/4 cup water in a small saucepan. Bring to a simmer, stirring to dissolve the sugar. Turn off the heat and let cool to room temperature. Discard the strips of zest.
Finely grate the zest from the remaining 2 limes and set aside. Juice all 3 limes and blend the juice, watermelon, prosecco, Campari and sugar syrup in a blender until smooth, about 1 minute. Pour into a 9-by-13-inch glass baking dish and freeze, 2 hours. Use a fork to scrape the ice crystals toward the center of the pan, then continue freezing, scraping every 45 minutes, until the mixture is no longer slushy, about 4 more hours.
Scoop into paper cones or cups. Drizzle with the peach nectar and sprinkle with the grated lime zest. Garnish with watermelon wedges.