Shiki is the helmsman of the Golden Lion Pirates, in addition to being the crew's captain. This is because the movement of his ship is controlled and levitated in the air by his Fuwa Fuwa no Mi powers. Any changes in course must be relayed to Shiki for him to conduct the change in trajectory.
The Strawhats do not offically have a helmsman, but the most common people seen steering the ship are Nami, Usopp, or Chopper in his human form. However, Franky and Sanji have also been seen steering the Thousand Sunny many times. Jinbe has helmed the ship in his current capacity with the Straw Hats, and has demonstrated tremendous skills as a helmsman, being able to guide the Thousand Sunny into a small "Green Room" within the giant sentient waveBig Momcreated, enabling the ship to surf away from the crushing waters safely; Nami commented that Jinbe's skills in controlling a sloop ship as an extension of his body qualifies him as a helmsman of such a caliber she has never seen before.