I would use the shoulder, but not right next to the curb, about middle of the shoulder. Then when right turn lanes start to come up I would transition (and use hand signals) when traffic allows to take the turn lane completely, then transition again when traffic allows to take the through lane nearest to the turn lane, once clear of the intersection make my way back to the shoulder. If traffic does not allow you to transition from the turn lane to the through lane simply stay in the turn lane moving closer to the left side of the lane and cross the intersection. If traffic is a nightmare and won't allow you to transition from the shoulder to take the turn lane sometimes it's safer to get to the intersection, dismount and walk at the light. If you use hand signals, most of the time cars will let you through (merge), so walking across the intersection should be a rare event.
Another IF, if you can keep up with the flow of traffic then it's safer not to use the shoulder and take the main right lane and keep up with the traffic, if you cannot keep up then move to the shoulder otherwise you will be impeding traffic and that is a ticketable offense.