I'm Poincare and, after consultation with Viviani, I make clear to Nicholas II in no uncertain terms that there is no defense for one government bumping off a leading figure in another. France stands with Austria.
There was a second "blank check", which has been memory holed, when French President Poincare and Prime Minister Viviani visited St. Petersburg during the July crisis. We still don't know exactly what their conversations with Russian officials consisted of. We do know that they did nothing to prevent a war, and while Viviani did not want war, Poincare was both brilliant and one of the few people in power in any capitol who definitely did want a war.
I agree that Russia backing Serbia was the key event, because although the unpopular Russian government feared getting even more unpopular if they backed down, backing down would only have resulted in a loss of faith. Germany would have diplomatically been completely isolated if it had not backed Austria-Hungary. But I'm not sure if it was really Nikolai II's call, or if the hardliners in the Russian government wouldn't have found a way to remove him. But I think Russia backs off if the French had made it clear that this was the wrong diplomatic crisis to take a stand on. And Poincare was key on this because he was the most hardline politician in France.
If you want another single person, Edward Grey is a possibility. He ran British foreign policy unsupervised, the last Foreign Secretary to do so (and there was a reason why he was the last one). He could have pulled back the French with a firmer line that Britain was sitting this one out, or prevented the invasion of Belgium by Germany with a firmer statement of support for France. Either course would have been better than what happened. But Grey could have prevented a world war, but not a war between the Teutonic powers and Germany, so I think Poincare was in a more critical position.
One reason I leave out the two Central Powers is that Germany and Austria-Hungary both had very decentralized governments, they were both after all sort of federations. In fact, a big problem both countries had in 1914 was that they took a long time to coordinate policy within the Germany and Dual Monarchy governments, and part of the governments would undercut the other. If I had to take one person or one position in the Central Powers, it would have been the Germany army chief of staff (Molkte the Younger). Someone ASOPed back into that position could have not undercut the other parts of the German government to diffuse the crisis, and could have called off the invasion of Belgium and remained on defense in the West. This probably at least limits the war, at least in 1914.
