Shuck the oysters and reserve the juice.
Put the cucumbers, ginger, seaweed, sugar and lemon juice in a blender and purée until smooth. Strain through a fine sieve, then mix in the tonic water. Season with salt and white pepper, then pour into a shallow tray and freeze for 4 hours.
Combine the sesame seeds, nori, shiitakes, wasabi and dashi in a spice grinder and pulse to mix finely.
Scrape the granita with a fork to make crystals and spoon over the oysters. Scatter with sesame mix.