Marinate the shrimp: Combine oyster sauce, soy sauce, rice wine, sesame oil, ginger, and sugar in a medium bowl. Add shrimp and toss to coat. Cover with plastic wrap and set aside to let rest at room temperature for 20 minutes.
Prepare the fried rice: Combine oyster sauce, soy sauce, rice wine, sesame oil, and sugar in a small bowl; set sauce aside.
Put rice into a bowl and use your hands to break up any clumps; set aside. Heat a wok or a 12-inch nonstick skillet over high heat until hot. Add 1 tbsp. oil and swirl to coat cooking surface. When oil begins to smoke slightly, add the eggs and stir vigorously to scramble until eggs are medium firm, about 1 1⁄2 minutes. Transfer eggs to a plate and cut into small pieces; set aside.
Wipe out wok or skillet with a dry towel. Heat over high heat until hot. Add 2 tbsp. oil and swirl to coat cooking surface. Drain shrimp, discarding marinade. Add shrimp in a single layer and cook, flipping once, until pink, about 2 minutes. Add ham and stir-fry for 1 minute. Transfer shrimp and ham to a plate and return the wok or skillet to the heat. Add remaining 2 tbsp. oil to pan, swirl to coat, and add the rice, using a spatula to spread it into an even layer. Cook rice over high heat for 6 minutes, stirring every minute. Add reserved sauce and stir-fry until rice is coated with sauce, about 1 minute. Mix in reserved eggs, shrimp-ham mixture, and scallions and cook for 1 minute. Transfer fried rice to a warm platter to serve.