In a large skillet, melt butter over medium-high heat. Add red onion, green onion, capers, remaining 1 teaspoon salt, and remaining 1 teaspoon pepper; cook until onions are tender and beginning to brown, about 6 minutes, stirring occasionally. Add garlic and cook for 1 minute more, stirring frequently. Stir in wine and lemon juice. Reduce heat to medium-low, and simmer until alcohol is cooked out, 3 to 4 minutes. Add shrimp and cook until just cooked through, 1 to 2 minutes per side. Remove shrimp from pan and set aside on plate. Add reserved spaghetti squash to pan, stirring to combine with vegetables. Fold in Parmesan and return shrimp to the skillet. Garnish with additional Parmesan and green onion, if desired. Serve immediately.