Place Snapper fillets in a large skillet. Add 1/2 cup wine and enough water to just cover the fillets. Bring to a boil over high heat. Reduce to a simmer, turn the fillets over, cover and cook for 5 minutes. Remove from the heat.
Meanwhile, heat oil in a medium skillet over medium-high heat. Add shallot and cook, stirring, until fragrant, about 30 seconds. Add the remaining 1/2 cup wine; boil until slightly reduced, about 1 minute. Stir in lemon juice and capers; cook 1 minute more. Remove from the heat; stir in sour cream and salt. To serve, top the Snapper with the sauce and garnish with dill.