Remove the seeds from the cucumber and cut into 4-inch spears.
Prepare a sheet tray or a shallow bowl with hot water. Working one at a time, dip the rice paper in the water until pliable, but not floopy, about 15 seconds. Transfer to a cutting board and blot with a paper towel.
Arrange the lettuce and cucumbers on the bottom third of the wrapper. Spread out a quarter of the razor clam salad and top with basil leaves.
Fold the left and right sides inward, then tightly roll the wrapper away from you. Repeat with remaining wrappers and filling.