Peel cucumbers and slice thin. Sprinkle with salt and let stand for 10 minutes.
Combine the rest of the ingredients. Press excess liquid out of the cucumbers using a paper towel. Stir the cucumbers into the sour cream mixture.
Remove crusts from bread and cut into halves or quarters (do what you think makes sense depending on the size of the bread pieces you have).
Spread a thin layer of the filling onto each sandwich.