Take the cucumber and peel it in long strips. Then, using a mandolin or a sharp knife, cut the cucumber into thin 1/8-inch slices. Lay these slices on paper towels and lightly sprinkle them with salt. This step helps to remove excess moisture from the cucumbers. Allow them to sit for about 15-30 minutes to draw out the moisture. Afterward, gently pat them dry with fresh paper towels.
While the cucumbers are resting, prepare the spread. In a medium-sized bowl, use a handheld mixer to combine the softened cream cheese, Greek yogurt, mayonnaise, dill, chives, lemon juice, garlic powder, and salt until smooth and well-blended.
Spread one side of each bread slice with the herbed cream cheese mixture. Then, layer the cucumber slices onto half of the bread slices and season them with black pepper to taste. Place the remaining bread slices, cream cheese side down, on top to form sandwiches.
With a sharp Chef's knife, cut each sandwich into quarters by pressing down through the bread to the bottom. This will yield 16 small sandwiches. You might need to gently adjust the cucumber slices as they may shift a bit during cutting.
Serve the sandwiches immediately and enjoy!