Put the oysters and their juice into a small non-reactive saute pan. Cook over moderate heat for just a minute or until the edges of the oysters curl very slightly. Lift the oysters out of the pan with a slotted spoon and set aside, keeping warm.
Increase the heat and reduce the oyster juice, adding the sauerkraut juice plus a squirt of lemon juice. When reduced by about 1/3 add the cream and butter. Continue to reduce adding the sauerkraut until the sauce is fairly thick.
Return the oysters and whatever liquid they have given off to the pan just to reheat. Add chives and dill. Spoon back 1 oyster and a little sauce into each warmed oyster shell.
Top with a tiny bit of caviar.