Exactly what it says in the thread title... what is the latest plausible date up to which the development of nuclear weapons can be delayed?
I´m thinking that, had then nuclear physicists in Nazi service decided to take their research in a direction not prone to be weaponized, or agreed among themselves to keep the weapons potential of their research secret, because they did not want Hitler and his fellows to have such an awesome weapon, there would have been no Nazi nuclear bomb project.
Without a Nazi project trying to develop nuclear weapons, Leo Szilard will not write that letter to President Roosevelt, Einstein not sign it, and there will almost certainly be no Manhattan Project, and thus no US nuclear weapons.
Now, this sounds all fine and dandy (read the Protect and Survive timeline to see why), but what are the consequences? No Hiroshima and Nagasaki means WW2 in the Pacific ends in one of three ways - Japan is starved into surrender by blockade, Japan is firebombed down to bedrock, or Japan is invaded. Either way, lots and lots more Japanese die through starvation, ground combat or bombing - and in case of the invasion, a lot more Americans as well.
Then, once WW2 is over, no nuclear weapons means there is one less incentive for Stalin not to start WW3. In the worst case, WW3 kicks off in the late 40s or early 50s; in the best base, the Soviet have one less reason not to intervene in Korea. In any case, the Cold War might get uncomfortably warm - and then perhaps rumors that Stalin has begun a project to develop nuclear weapons drives Einstein to write a certain letter to President Truman...