Trim ends from cucumbers and cut crosswise into 24 (3/4-inch-thick) rounds. Scoop a 1/2-inch-deep depression from one side of each round with a small melon-baller, forming little cups. Drain cucumbers, cup sides down, on paper towels for 15 minutes.
Beat cream cheese, chopped dill, lemon zest, lemon juice, and black pepper together in a bowl. Spoon 1/2 teaspoon cheese mixture into each cucumber cup. Top each cup with 1 salmon strip and 1 dill sprig.