Put the eggs in a saucepan and cover with cold water by 1 inch. Bring to a boil; reduce the heat to low and simmer 10 minutes.
Drain the eggs and transfer to a bowl of ice water to cool; peel and halve lengthwise. Scoop out the yolks and transfer to a bowl.
Add the mayonnaise, sour cream, horseradish, mustard, 1/4 teaspoon salt and a few grinds of pepper; mash until smooth. Stir in the diced cucumber and the parsley, chives and dill. Spoon the filling into the egg whites; top each with a cucumber wedge. Refrigerate 30 minutes to 1 hour.