Trim the ends of the cucumbers, slice them lengthwise in half, remove the seeds, and cut crosswise into paper-thin slices. Place in a bowl. Combine the sugar, rice vinegar, ginger, and salt and stir until the sugar dissolves. Add to the cucumbers, toss lightly, and cover with plastic wrap. Let marinate for at least 30 minutes, or longer if possible, in the refrigerator, tossing occasionally.
Place the fish steaks in a bowl. Combine the marinade ingredients, add to the fish, and toss to coat. Cover with plastic wrap and let marinate for 30 minutes at room temperature, turning several times.
Prepare a very hot fire for grilling, and place the grill about 3 inches above the coals. Arrange the fish steaks on the grill and cook for about 4 to 5 minutes on each side, basting occasionally with the marinade, until the fish is opaque all the way through. Transfer to serving dishes. Serve the cucumber relish on the side or spoon it over the fish.