In a medium bowl, combine the softened cream cheese, dill, lemon juice, garlic powder, salt, and black pepper. Mix until smooth and well combined.
Lay out the slices of bread on a clean surface. Spread a generous layer of the cream cheese mixture on four slices of bread.
Arrange the cucumber slices evenly over the cream cheese on each of the four slices. If using, add a few radish slices on top of the cucumbers.
Top each with the remaining slices of bread to create sandwiches.
For a neat presentation, trim the crusts off the sandwiches and cut them into quarters or triangles.
If time allows, chill the sandwiches in the refrigerator for about 30 minutes before serving to enhance the flavors.