Place the cucumber, radish, shallot, vinegar, salt, and pepper in a small bowl. Stir to combine. Refrigerate until ready to serve. The mignonette can be made up to 1 day ahead of time. To serve, place the ice in a food processor and pulse a few times until slightly crushed. Spread the ice out onto a large tray or oyster plate and place the oysters on top of the ice. Serve the oysters immediately with a ramekin of the mignonette sauce, a small spoon, and a few oyster forks.