Place watermelon in a blender; process until smooth. Pour pureed watermelon into a sieve over a large bowl, pressing with the back of a spoon to extract as much liquid as possible; discard solids. Combine 3 cups watermelon juice, tequila, Triple Sec, lime juice, and salt in a pitcher; stir with a whisk. Gently stir in club soda. Serve over ice with lime wedges.