Gibb-

"we were soon slipping up to our port"

There's reference to a tug, I believe, which implies that they were using a capstan shanty for hauling up the anchor. Then a hawser would be passed from the tug to the ship (or the other way around) and they would have been towed up to the docks. Some docks might have capstans installed to warp the ships in for their final mooring, but the crew aboard ship wouldn't be singing shanties for the dockyard gang who was doing that work.

Charley Noble