Not sustainable at all because they use helium for lift.
Currently we can't manufacture helium in meaningful quantities, so the helium we get comes from fossil fuel extraction "natural gas" as it comes out of the ground contains all sorts of gases including helium. The US government has long funded some gas extraction/purification plants collect and purify the helium for sale (wikipedia), because it's expensive to do that and hence not profitable, but the government wanted the helium initially for airships and later as a strategic resource.
Your question seems to focus on bulk cargo movement, which today is shipping containers or bulk fluids (coal and ore are handled as fluids in this context). In terms of both mass and volume the overwhelming majority is moved by sea. On this graph just note that the air axis goes to 200, the sea axis to 18,000 - 90x as much. The bulk of my answer in the headings below compares airships to waterships. The short answer is: airships do badly.
Compared to other aircraft
Helicopters are crazily inefficient in energy terms and their lift capacity and range is a joke. A truck can carry more, further, faster, cheaper and more reliably. A big helicopter can carry about 10 tonnes about 100 kilometres which is not really "cargo carrying" in modern terms, it's more of a specialised lifting task. Fixed wing aircraft are better on both counts, using less fuel and travelling both further and faster. A large fixed wing aircraft can carry about 300 tonnes for 15,000 kilometres, where the high end for watercraft is 120,000 tonnes for 20,000 kilometres (and the energy cost is at least a thousand times lower). An airship that can match fixed-wing aircraft lift capacity and range is useful, but bulk cargo capacity is not the advantage.
Air propellers can be more efficient than water ones 80%+ vs ~70% in both cases increasing with diameter and decreasing with speed.
Unfortunately the airship has to push a lot more air out of the way for a given cargo weight than a water vessel has to push water. A ship gets 1 tonne of lift for every cubic metre of water it displaces, while a helium airship gets about 1kg per cubic metre. So roughly speaking an airship will have a thousand times the volume of an equivalent water ship (at this level we can assume both ships have no mass). That's enough that we can ignore air drag on the water ship and just look at water drag.
At low speeds with laminar flow the drag equations are fairly simple and the dominant factor is the viscosity of the fluid. Both airship and water ship designers work quite hard to stay in this zone. Wikipedia has a list, with air typically about 18μPa.s and water 1000 μPa.s (50x as high). Since the airship is 1000x the volume it'll be about 10x as large in each dimension. Drag here is determined by frontal area (basically, how much fluid has to be shoved out of the way) so the airship has 100x the frontal area and 100x the drag, but air is only 1/50th the viscosity. Overall, the airship faces twice the drag of the water ship.
On a global scale air moves less predictably than water, and faster. Ocean currents just don't change as much as winds do. That means that airships face more vigorous weather, less predictably and hence have less ability to avoid it.
This also means that the airship, being both really big and really lightweight, usually can't just be tied down in a storm - the wind would tear it apart. So airships need to be docked inside a hangar. A really, really big hangar. Or they need to be semi-rigid so they can land, deflate, and park in a smaller hangar. Or just fly with the storm and come back afterwards, from wherever they got blown to. None of these is cheap, and make the airships less reliable than modern transport systems prefer.
Loading and Unloading
Both types of ship require docks, and the docks have to be large and strong. But again, the difference in lift means that an airship has to be 1000x as big for the same cargo capacity. Even if the dock is just a post with a rope in the middle of a circular clearing, the airship is 10x as long so the clearing has to be 100x as large. For temporary sites, the airship can hover and winch things down. Similarly, a water ship can use a crane to unload itself. Water ships generally don't do this because they carry so much more than an airship does (a "medium sized" water ship might carry 100,000 tonnes of cargo) while a really big airship carries 160 tonnes - note the absent "000" on the second number). That factor of 1000 conveniently means that an airship is likely to be about the same size as a water ship. So they could use the same docking areas. But with a thousand times more cargo in the water ship.