Thaw fish, if frozen. Rinse fish and pat dry with paper towels. Measure thickness of fish. Set aside.
Chop enough of the cucumber to equal 1/2 cup. Thinly slice the remaining cucumber; set aside.
In an ungreased 10-inch skillet stir together the orange peel, orange juice, carrot, and salt. Bring the mixture to boiling. Carefully add fish to skillet. Return the mixture just to boiling; reduce heat. Cover and simmer for 4 to 6 minutes per 1/2-inch thickness of fish or until the fish flakes easily when tested with a fork.
Place cucumber slices on a platter. Use a slotted spatula to transfer fish to platter atop cucumber. Cover with foil to keep warm.
For sauce, in a small bowl stir together the cornstarch and water. Stir into the mixture in the skillet. Cook and stir until mixture is thickened and bubbly. Cook and stir for 2 minutes more. Stir in the chopped cucumber. Spoon the sauce over fish. Makes 4 servings.