Whisk eggs and milk together in a small mixing bowl, then move to a shallow dish.
Whisk together flour, salt, black pepper, and cayenne pepper in a mixing bowl, then move to a separate shallow dish or plate.
Dip shrimp into beaten egg mixture, then dredge in flour mixture.
Heat oil in a heavy bottom pan or Dutch oven until oil reaches 380 degrees F.
Line a plate with paper towels, set aside.
Drop coated shrimp into heated oil in batches, cook for about 3 minutes, then remove from oil and place on the prepared plate.
Move shrimp to a mixing bowl, drizzle wing sauce over top and gently toss to coat.
Serve warm with lemon slices and dressing of choice, if desired.