For the mignonette: Combine the vinegar, chipotle, peppercorns, shallots, cilantro, and honey. Season to taste with salt and pepper and chill.
For the relish: In a medium saucepan, combine the juices, ginger, garlic and honey and bring to a boil over high heat. Reduce by half and set aside to cool. When the syrup has cooled to room temperature, add the shallots, cilantro, lime segments, and zest. Season to taste with salt and pepper and pour into a nonreactive bowl.
For the horseradish sauce: Combine all ingredients.
For the oysters: Serve the oysters on ice with the mignonette, relish and horseradish sauce.