In a medium mixing bowl, whisk together the softened cream cheese, mayonnaise, chopped dill, lemon juice, garlic powder, salt, and black pepper until the mixture is uniform and creamy.
Using a serrated knife, remove the crusts from all eight slices of bread.
Lay the bread slices out on a clean work surface and spread an even layer of the cream cheese mixture onto one side of every slice.
On four of the slices, arrange the cucumber slices in slightly overlapping rows to cover the entire surface area.
Place the remaining four slices of bread on top of the cucumbers, cream cheese side down, to close the sandwiches.
Press down lightly on each sandwich to secure the filling, then cut each sandwich diagonally twice to create four small triangles.
Serve immediately at room temperature or refrigerate for 30 minutes to firm before service.