Add water, sugar, ginger, and chili to a small saucepan set over medium heat. Stir until sugar dissolves. Turn heat to the lowest setting and steep for 20 minutes, stirring occasionally. Strain into a jar with a tight-fitting lid and set in the fridge to chill. Ginger simple syrup will keep for several weeks in the fridge and can be used for cocktails, lemonade, or the beverage of your choice. Save 4 slices of candied ginger for the watermelon cooler; the remaining candied ginger should be devoured on the spot. (If you'd like, toss candied ginger in sugar to coat.)

To make coolers, layer ice, watermelon chunks, lime juice, 4 reserved ginger slices, and 2 tablespoons spicy ginger simple syrup in the pitcher of a blender and blend until smooth and frothy. Pour into chilled glasses, garnish with a lime wedge, and serve.