Rinse snapper under cold water, and pat dry. In a shallow bowl, mix together olive oil, lemon juice, rice vinegar, mustard, honey, green onions, and ginger.
Heat a non-stick skillet over medium heat. Dip snapper fillets in marinade to coat both sides, and place in skillet. Cook for 2 to 3 minutes on each side.
Pour remaining marinade into skillet. Reduce heat, and simmer for 2 to 3 minutes, or until fish flakes easily with a fork.