For the Oysters:
Begin by shucking oysters. Find a durable, thick cloth and fold it over several times to create a square; this will steady the oysters as you shuck them and also protect your hand. Using the towel as a mitt, hold the oyster firmly on a flat surface. Insert the tip of your oyster knife between the shell halves, and work it around 1 side to the other as you pry it open. Using the knife, cut the muscles away from the top, flat shell, bend the shell back, and discard it. Run the knife underneath the oyster to detach it completely, but leave it in its shell (take care not to cut the meat itself). Nestle the oysters in a bed of crushed ice or wet rock salt to keep them steady. Serve immediately.
For the Cucumber Mignonette Sauce:
In a small bowl, combine the rice wine vinegar, shallots, ginger, cucumber, sugar and black pepper; mixing with a fork. Cover and chill for at least 1 hour or up to the day before you plan to serve, to allow the flavors to come together. Serve with raw oysters.
For the Cocktail Sauce:
Mix ingredients in a blender to combine. Cover and refrigerate until ready to use.