eking out fuel

It sounds like they were alluding to a situation where the ship was stranded, and the people had to ration both the fuel and the fuel.

I would imagine wood, or coal or whale oil, burned for heat, light, and cooking. The days of the great wooden ships ended around the time of the American Civil War, I think.

Yes, I will concoct something.

The age of sail did not end until well after 1900--although wooden ships were used less and less in national navies and commercial fleets. Wooden ships are common to this day in coast-wise trade in Africa and Asia. However, the point is, wooden ships remained common until the end of the 19th century.

By the way, in this context, fuel would almost certainly refer to fire wood. Whale oil was far too valuable a commodity to burn for fuel on a ship, and coal was not commonly available, even in the age of the steamship, as a cheap source of fuel. Those who burned coal to fire boilers for steamships got it at a reduced price because they literally bought it by the ton. In such a context, referring to "ancient wooden ships," the only rational inference is fire wood.

Arctic exploration in the age of sail and wooden ships only truly begins in the mid-18th century, with Anson. There is, however, no good reason to assume that this author knows this.