Scrub the clams under cold water with a stiff brush to remove the dirt. Next, find a durable thick cloth and fold it over several times to create a square; this will steady the clams as you shuck them and also protect your hand. Using the towel as a mitt, hold the clam firmly in the palm of your towel-covered hand; have a small bowl handy to catch the delicious juice. Insert the tip of a clam or oyster knife between the shell halves, and work it around one side to the other as you pry it open. Using the knife, cut the muscles away from the top shell, bend the shell back, and discard it. Run the knife underneath the clam to detach it completely, but leave it in its shell (take care not to cut the meat itself.) Tip out the clam juice into the bowl and pour it back over the shucked clams. Nestle the clams in a bed of crushed ice or rock salt to keep them steady. Spoon the cucumber mignonette on top and serve as part of a raw shellfish bar.