Rinse the cucumber, and cut 2 thin slices for garnish. Peel the remaining cucumber and the shallot. Coarsely chop both, then puree completely in the blender with the dill, yogurt, and the milk. Season to taste with salt, pepper, Tabasco, and Worcestershire sauce. Stir until completely combined.
Pour the shake into two glasses, garnish with the reserved cucumber slices and dill, and serve immediately.