Halve cucumber crosswise and thinly julienne lengthwise, preferably with a mandoline or other manual slicer, working around core. Discard core.
Stir together sour cream, horseradish, and salt and pepper, to taste.
Divide bread into 4 stacks and cut stacks into 1 1/2-inch squares with a serrated knife, discarding crusts. Spoon 1/2 teaspoon sour cream onto center of each bread square, then top with a folded piece of salmon.
Top salmon with a small amount of cucumber, twirled into a mound.
Cooks' notes: Cucumber can be julienned 2 hours ahead and chilled, covered. Bread can be topped with cream and salmon 6 hours ahead and chilled, covered with dampened paper towels and plastic wrap. Top with cucumber just before serving.