Using a blender, puree the watermelon; you will need 4 cups watermelon puree. In a large saucepan, bring 1 cup watermelon puree, the sugar and lime or lemon peel to a simmer over medium-low heat, stirring until the sugar dissolves; season with the salt. Pour in the remaining 3 cups watermelon puree, then whisk in the corn syrup until incorporated. Pour the watermelon mixture into a 9-inch metal cake pan and freeze until firm, about 4 hours or overnight. Let the frozen watermelon soften at room temperature for 5 to 8 minutes. Using a butter knife, break up the frozen puree into 2-inch pieces. Transfer the pieces to a food processor in batches and pulse until smooth. Store the sorbet in a freezer-safe container for up to 1 week. Let stand for 5 minutes before scooping.
