In a medium bowl combine the relish ingredients, including ½ teaspoon salt and ¼ teaspoon pepper. Mix well and let stand at room temperature for at least 30 minutes or up to 4 hours.
In a medium bowl whisk the cornmeal, flour, baking powder, and ¾ teaspoon salt. In a large measuring cup whisk the milk, butter, and egg. Pour the wet ingredients over the dry ingredients and whisk gently until a smooth batter forms, being careful not to over mix.
Prepare the grill for direct cooking over medium heat (350° to 450°F). Preheat a griddle over direct heat for about 10 minutes.
Lightly brush the shrimp with oil and season evenly with ¼ teaspoon salt and ¼ teaspoon pepper. Coat the griddle with 2 tablespoons oil.
Working in batches, ladle ¼ cup of the batter for each cake onto the griddle, flattening each cake gently with the back of a spoon. Cook over direct medium heat, with the lid closed, until the corn cakes are browned on both sides and cooked through, 3 to 5 minutes, turning once. At the same time, grill the shrimp over direct medium heat until they are just firm to the touch and opaque in the center, 3 to 5 minutes, turning once or twice.
To serve, divide the corn cakes among serving plates and dollop about 2 teaspoons of sour cream on each cake. Top with one or more shrimp (depending on the size you purchased). Drain and spoon the relish alongside each cake. Garnish with cilantro, if desired. Serve immediately.