To make cabbage and ginger tsukemono, place cabbage in a large colander over a bowl, add salt and toss to combine. Stand for 20 minutes. Meanwhile, combine, sugar, vinegar and ginger in a small saucepan over medium heat and stir until sugar dissolves (5-6 minutes). Cool. Squeeze moisture from salted cabbage and place in a bowl. Pour over vinegar mixture and toss well to combine. Refrigerate for 1 hour or until chilled.
To make radish, cucumber and lime dressing, place ingredients, except radish and cucumber, in a blender and blend until smooth. Transfer to a bowl with radish and cucumber, refrigerate for 30 minutes to chill. Adjust the seasoning of the dressing to taste; it should be equally sweet, sour and salty.
Arrange oysters over rock salt (or crushed ice) on a large platter with the two dressings in small bowls on the side. Top half the oysters with one dressing and the half with the other.
