High guys. First post, just registered a couple days after seeing this thread and lurking for a few minutes. I had to say something!
On the subject of Airships:
They would totally reign supreme in the air...seeing as they are the only thing up there. Infrastructure historically designated for airplanes would be shifted to airship development. Even incidents like the Hindenburg disaster would just be a bump in the road compared to the historical “end” of airship use. Soon, helium airships would crowd the skies. They would take on passengers in open fields outside of cities near train stations, but soon demand would increase and it would become attractive for builders to construct massive skyscrapers in the centers of cities that could then be used as docking ports for airships. This would increase revenue for the owners of the skyscraper and encourage even larger structures that can take on my airships at one time. The major increases in passenger use between 1919 and 1939 that would have been for airplanes would instead be for airships. Militarily I think we would see a lot of innovation. Nothing can really reach an airship at high altitude save for flak shells. Airplanes usually shot down bombers during WW2, but in this history the airships are going to have to be countered by other airships. The airship arms race would lead to massive hangers being built, camouflaged to look like small mountains or hills. Airships would soon use light artillery pieces all over, then they would get up to bigger 5” guns. Large 10” naval guns would require truly massive airships to support that load. Due to the superior ranges of airships, air to air battles would take place all over the globe if two major nations fought it out.
Moving away from airships:
There is now no more use for aircraft carriers. Even though airships may effect the superiority of sea based vessels slightly, they won't have near the effect if aircraft had been invented. Instead of vast navies of aircraft carriers replacing battleships towards the 1930's and 40's, there would instead be bigger and better battleships. The biggest battleship ever, the Yamato, weighed in at slightly over 70k tons. Soon we would start to see even larger battleships that weigh in at over 100k tons. Some nations would build ever larger battleships capable of fielding ever larger guns. Not needing smaller anti-air guns would make more room for larger batteries of intermediate guns. Between 1895 and 1950 American battleship tonnage increased amazingly fast. By 1960 there would easily be 150k ton battleships cruising around. Missiles would probably lead to the end of massive battleships, but then again they said the same thing about tanks which turned out not to be true. If no form of “complex flight” including missiles is allowed, then battleships would dominate.