But not nuclear arms.
Developing nuclear arms is EXPENSIVE. Even with proof of concept in place. Germany failed, Britain needed till 1952...
Easy PoD. Gavrilo Princip misses. Franz Ferdinand dies natural causes in 1950, aged 86 like Franz Joseph - and Emperor of Austria-Hungary. His funeral in Vienna is attended by Empoeror Wilhelm III (Wilhelm II died natural causes in 1941 as OTL) and Emperor Alexis of Russia.
With military budgets as percentage of GDP never exceeding the 1913 levels through 20th century, how much would Wilhelm III-s Germany invest into checking the speculations of German nuclear physicists and science fiction writers about theoretical possibility of nuclear explosion?
Even people deep into the topic can reasonably discuss the possibility of a reactor meltdown due to runaway chain reaction (uranium ores in Bohemia are in Austria), but conclude that a bomb is impractical because it would predetonate and fizzle at a small yield. The theoretical possibility of enriching a critical mass of uranium... with no war expected and elected Reichstag keeping Reichswehr at short budget, no one will invest in checking and those who are aware of speculations can suspect it would fizzle anyway.
Developing nuclear weapons is expensive (approximately what an aircraft carrier costs to develop and build), when you are in a hurry with your economy drained by WW I and WW II. A more modest amount of funding (such as what was spent on a battleship) from a national economy that hasn't been crippled would manage it in a decade.
Nations would invest in nuclear weapon research even when at peace, military budgets would be smaller but with a higher percentage on R&D.
One big delay for Britain was they provided the Manhattan Project with their nuclear research, scientists and uranium while anticipating that America would reciprocate by giving Britain the results of the project. If the British had done it on their own, it was expected they would have managed by 1947 (Churchill knew that would be too late, which is why he turned to America). If the United States had provided Britain with the results, then they would have had it the same year as America.
Germany failed because a lack of uranium, the belief in "German physics" , the loss of the majority of their best scientists, and other WW related issues. No WW I or WWII, then they would have not had those problems.
The
Frisch–Peierls memorandum was the first technical exposition of a practical nuclear weapon in 1940, but many scientists were capable of calculating the theoretical effects of fission on pure uranium. Once the basic model of the atom (
Rutherford model 1911 (later replaced by other models)) was developed, then it became inevitable that someone would eventually think of calculating those fission results. No one who calculated fission on pure uranium had the result of the bomb fizzling, many calculations were too high or too low but all gave the result of a successful nuclear detonation of kilograms of pure uranium. Once it is known that a pure uranium bomb will work, then it is a matter of costly experimentation to purify uranium (aka enrichment) and successfully engineer a viable design.
Many scientists (including the notable Niels Bohr) concluded a fizzle would result, but they were calculating the effects of unrefined (or limited refinement) uranium, not pure uranium.
Nuclear reactors can be used to enrich uranium, and some of the early designs did it unintentionally. Any use of nuclear power will result in the realisation that bombs are perfectly possible. Opposition to nuclear power began when civilians saw photographs of Japanese who suffered irradiation, and grew with disasters like Chernobyl. Without those two events, nuclear power would be more widely used.
British and German progress was crippled by WW I, research into pure science (e.g. nuclear physics) had it's funding massively cut and scientists were recruited/conscripted into the military. Wartime secrecy, censorship and restrictions on international cooperation also significantly slowed research.
Without WW I, both nations could have developed the nuclear bomb in the 1930s. Whether they would have built and tested one depends on the international scene, but they would have had the design.
Henry Moseley (killed in WW I battle of Gallipoli) empirically produced important information about atoms (including heavier ones like uranium) by hitting them with electrons and x-rays. With the discovery of protons (1920) , if he had lived then it is highly likely that he would have continued his experiments but with protons.
One major risk is the lack of war-related secrecy would mean that a substitutional amount of the nuclear physics behind the bomb would be public. At first details were hidden to keep the advantage of being the only one with the weapon, and then it was because of the destructive nature of the weapon. No war means the technology becomes classified at a later point in development.