Divide enough ice between 4 glasses. In a pitcher, stir together the tomato juice, vodka, horseradish, 2 tablespoons curry powder, 2 tablespoons celery salt, Worcestershire sauce, lime juice, and hot sauce. Pour the resulting liquid over the ice in the glasses.
Toss the remaining 1 tablespoon curry powder and 1 tablespoon celery salt together on a plate. Dip the cucumber pieces in the spice mixture and dunk them into each glass.