Wash the English cucumber and slice it into very thin rounds. Place the slices on a paper towel and sprinkle lightly with salt. Let them sit for about 10 minutes to draw out excess moisture, then pat them dry. This prevents the sandwiches from becoming soggy.
In a medium mixing bowl, combine the softened cream cheese, chopped dill, minced chives, lemon juice, and garlic powder. Use a whisk or a fork to blend everything until the mixture is light and fluffy. Season with a pinch of salt and black pepper according to your preference.
Lay out the bread slices on a clean work surface. If you like, spread a very thin layer of butter on one side of each slice; this acts as a barrier to keep the bread crisp. Use a knife to carefully remove the crusts from each slice of bread.
Spread a generous layer of the seasoned cream cheese mixture over each slice of bread. On half of the slices, layer the cucumber rounds in slightly overlapping rows. Top with the remaining bread slices, cream cheese side down.
Using a sharp serrated knife, cut each sandwich into four triangles or squares. Alternatively, use a circular cookie cutter for a round shape. Garnish the top of each bite with a tiny sprig of fresh dill or a sprinkle of paprika before serving.