For the Chipotle Mignonette: Combine all ingredients together in a small bowl. Season with salt to taste. Refrigerate for 1 hour.
For the Ginger-Lime Relish: In a medium saucepan, combine the juice, garlic, ginger and honey and bring to a boil over high heat. Reduce by half and set aside to cool. Peel the limes and julienned the zest. Separate the flesh into segments. 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 non-reactive bowl. Serve at room temperature on the oysters.