Use a sharp knife and cutting board to slice the watermelon into evenly thick strips, approximately 1/4 inch wide, resembling fries. Arrange the watermelon fries on a serving plate and keep chilled until ready to serve.
In a small mixing bowl, combine the grated shredded coconut and coconut milk. Add the fresh lime juice and stir well with a small spoon until the mixture is smooth and slightly thickened. The dip should have a creamy consistency and a bright citrus aroma.
Serve the chilled watermelon fries on a platter alongside the coconut lime dip. For presentation, you can arrange the fries in a parallel line or cluster for visual appeal.
Optionally, garnish the dip with a small sprinkle of extra grated coconut or a lime wedge for added visual contrast and flavor.