Remove rind and cut watermelon into large pieces. (If possible, work over a large bowl to catch juices.) Purée chunks in a blender until smooth. Set aside.
In a large bowl, toss all remaining ingredients. Pour watermelon purée and any juices over vegetables, cover, and refrigerate until well chilled, at least 1 hour. Taste and season with more salt and pepper or jalapeño. Serve very cold.