Whisk eggs, milk, hot sauce, and Cajun seasoning together. Set aside. Toss shrimp in oil and pepper. Heat a large nonstick skillet over medium-high heat. Add shrimp and cook until opaque, about four minutes. Drop in butter, reduce heat to medium and, once butter is melted, pour egg mixture over shrimp, stirring to evenly cook the eggs. Fold in sausage and cook eggs to desired doneness. Serve over Texas toast or English muffin.