Heat the oil in a skillet over medium-high heat. Add the onions, season with salt and cayenne, and cook, stirring, until the onions are soft, about 3 minutes. Add the shrimp and cook, stirring, until they turn pink, 2 to 3 minutes. Remove from the heat and set aside.
Combine the eggs, milk, baking powder, the teaspoon salt, and season with cayenne to taste. Mix well. Add the flour, 1/4 cup at a time, whisking until all is used and the batter is smooth. Season with hot sauce and Worcestershire.
Season the zucchini with salt and pepper. Add the shrimp mixture and the zucchini to the batter and fold to mix.
Heat the shortening in a heavy, deep pot or electric fryer to 360ºF. Drop the batter, a heaping tablespoon at a time, into the hot oil. When the fritters pop to the surface, turn to brown them evenly in the oil. Remove from the oil and drain on paper towels. Season with Essence and serve warm.
Makes about 2 dozen