In a large bowl, combine the watermelon and sugar and stir well to coat. Cover the bowl and refrigerate overnight. The next day, mix together the vinegars in a small bowl and stir. Add the vinegars to the watermelon, stir and place back into the refrigerator. On the third day, fine strain the solids out and store the shrub syrup in the refrigerator until ready to use.
For chili-basil syrup
Bring all ingredients to a slow boil. Allow to cool and fine strain (run through two strainers) into a container.
To make the watermelon shrub
Shake together all ingredients except the Topo Chico and double-strain into a Collins glass. Add ice and top with the Topo Chico. Lightly stir and garnish with a lime wheel.