Place first 5 ingredients in a blender; process until smooth. Cover and chill.
Thread 1 watermelon piece and 1 kiwi-fruit piece onto each of 24 skewers. Serve with sauce.
Note: To shape the kiwifruit as in the photo, cut a thin vertical slice off both ends of fruit, revealing the flesh. Peel by cutting vertical strips from one end to the other. Cut each kiwifruit lengthwise into quarters. Cut each quarter crosswise into thirds.