I will usually ride on, or just to the right of, the line between the straight-ahead lane and the right-turn-only lane. That position typically turns into the shoulder of the road on the other side of the intersection. If the road has no shoulder after the intersection, then I take the straight-ahead lane and ride as hard as I can to get to a part of the road that has a shoulder, as quickly as possible.
This is how I usually do it too