Put all of the watermelon pieces into a blender and blend until completely liquefied. Using a fine mesh strainer, strain the watermelon juice to remove all of the watermelon pulp, leaving you with only juice.
In a cocktail shaker, muddle the cucumbers a bit and then add in the St. Germain, vodka, and sugar. Shake well.
Pour the liquid evenly into 2 glasses filled with ice. Top the glasses the rest of the way up with club soda.