In a small bowl, whisk together the balsamic, shallot, salt and pepper. While whisking, drizzle in the olive oil to emulsify the mixture.
Place the feta cubes in a shallow bowl and top with about 1/3 of the vinaigrette. Gently toss to coat well. Set aside to allow the cheese to marinate while preparing the rest of the ingredients.
Place the shrimp in a shallow bowl and top with about 1/3 of the vinaigrette. Gently toss to coat well.
Heat a medium skillet over medium-low. Pour in the shrimp their marinade, cooking the shrimp until pink and cooked through, about 5 minutes total, turning once. Remove the shrimp to a plate and allow to cool to the touch.
Meanwhile, wash off and slice open the melon. Use a melon baller to scoop out 12 balls of watermelon, about 1” in diameter. Alternately, slice the melon into 1” cubes. Save remaining watermelon for another purpose.
When ready to skewer the ingredients, begin by threading on a shrimp. Next, gently wrap an arugula leaf around a melon ball/cube and thread it on the skewer, piercing the arugula on the top and bottom. Complete the skewer with a cube of the feta.
Place the skewers on a serving tray (either standing or laying flat), drizzle lightly with some of the remaining vinaigrette and serve. Any remaining vinaigrette can be served on the side or saved for another purpose.