Place the crème fraîche, onion, lemon zest and juice, dill, mustard, sugar, salt, and pepper in a large, nonreactive bowl and stir to combine; place in the refrigerator.
Fill a large saucepan two-thirds of the way with heavily salted water and bring to a simmer over medium heat. Meanwhile, prepare an ice water bath by filling a large bowl halfway with ice and water; set aside.
Add the shrimp to the simmering water and poach until pink, firm, and just cooked through, about 2 minutes. Drain and transfer to the ice water bath to cool. Drain the shrimp again, pat dry, and cut into small dice.
Remove the reserved dressing from the refrigerator and fold in the diced shrimp, radish, and cucumber. Season with additional salt and pepper as desired. Refrigerate until cold, at least 30 to 45 minutes. To serve, divide the shrimp salad among toasted rye bread slices or eat on rye crackers.