and making much headway against a strong headwind is going to take a lot of power with that much windage.
Just to clarify a common misconception about wind and "windage": many people seem to think that wind affects airplanes the same way as cars, needing more power to keep moving in a headwind. That is not the case. Airplanes fly in the air, they don't care about the ground. If that air happens to be moving, they move along with it. It's an extra speed vector to be added to airspeed, nothing more. Like walking on a conveyor belt, you don't get more or less tired (per minute) when walking at the same pace, but you do move more quickly or slowly depending on the direction of the belt. Airplanes don't "feel" crosswinds either, they just fly straight through the air, but end up moving sideways relative to the ground because of the addition of the two speed vectors.
The only reason why airplanes often use more power in a headwind, is because the pilot may elect to fly faster to (partially) compensate for the wind. An 80 kt airship in a 40 kt headwind will only have a ground speed of 40 kt, so the pilots may well choose to increase power to get a higher ground speed. The economic optimum speed for total fuel consumption over a given distance is at a higher airspeed in a headwind, and at a lower airspeed in a tailwind, simply because the math works out that way: the airship in a 40 kt headwind will get a 10% boost in ground speed (44 i.o. 40) for only a 5% boost in airspeed (84 i.o. 80), which shifts the economic optimum speed upward. But fuel consumption per minute at the same airspeed is the same no matter what the wind is.
So headwinds don't affect the airship any more than it affects a small plane with a cruising speed of 80 kts.
Changing gusts of wind are a different matter, of course. The plane or airship definitely does "feel" those.