Um, idk if this really counts as "sail", but heres what I got.
Lets take your airship. Assuming its sails are placed how you would see on like a galleon, remove them. Place them onto the side of the hull. Now them equal in terms of surface area, weight and structure if possible.
Now, you have 1 sail on each side of the ship, and you can pull in the sail or push it out. That part is very important.
Assuming you are facing exactly where the wind is going, both sails(extended the same percentage) will create equal drag on both sides so that the airship is pushed along the wind. Now lets say one of extended farther than the other, say the right sail is 70% exposed/extended while the left sail is only 30%. Now, the level of drag on either side is now unequal, imbalanced(insert thanos reference). Due to this, the airship will then veer to a desired direction, manipulated and controlled by how far extended each sail is.
Now, I think its pretty good, but it has a few limits.
for example,if turne enough, the rear of the ship( or any part of the ship) will block wind from the sail,and will normalize into the wind.I'll call this understeering
Now, if you made sails that the winds can push regardless of the ship orientation(say, having sails bigger than the entire ship not including sails) the difference of drag on each sail will be too big, and the ship will broadside(showing full side profile) the wind, both rendering both sails useless/ineffective at catching the wind, so no getting out of there until the wind rotates your ship into a position/orientation where the sails work, but your airship will probably have overturned, and crashed. I'll call this oversteering.
Now, assuming your smart enough not to under or oversteer, your ship should be able to veer left and right(or any direction, as long as placement of the sails allow for it).
Whether this would actually alter course effectively, idk. But good engineering?