Make the juice. Place a large bowl on the counter and place a fine-mesh sieve over it lined with a moistened paper towel. In a blender, purée the watermelon chunks, in batches if necessary. Pour into the prepared sieve and allow to drip until only foam and pulp remains on the top and the liquid has passed through. Do not press or squeeze the liquid through, just be patient—this could take about 20 minutes.

Discard the foam and pulp. Pour the juice (makes about 2 cups) into a pitcher and stir in vodka and schnapps.

Prepare the glass and serve. Pour the sugar on to a shallow plate. Use the lime wedges to coat the edge of each glass then coat the edges in the sugar by turning each glass upside down on the plate and twisting a bit, then gently shaking off the excess. Stir the drink again and serve in prepared glasses over crushed ice with a spritz of lime.