Cut watermelon in half, then use a melon baller or round teaspoon to scoop out flesh in round balls.
Reserve the balls, then use a spoon to scrape out any remaining watermelon flesh.
Fill mini watermelons with lemonade (or Sprite), as well as watermelon juice (about ⅓ cup) and vodka (1 ½ to 2 ounces), if desired. Add a few melon balls to punch.
Thread a lemon slice and more melon balls on a cocktail pick, then use to garnish punch along with a drink umbrella, if desired.