Are you suggesting that one of the first two guys get lucky?
Because, of course, the OTL assassination involved a gun.
My own first thought when I read this scenario: Mehmedbašić gets just a
little bit of luck when he throws his bomb. OTL, Franz Ferdinand was able to deflect the object, either by knocking it away (more likely) or by catching it and throwing it away, so that it exploded in the street behind his car with the only significant injury occurring to one of General Potoriek's aides, who got his face and hand cut up by fragments. Duchess Sophie, FF's wife, got scratched in the back of the neck by one of those fragments. TTL, we can assume that the Archduke was just that tiny bit slower and didn't manage to get the bomb far enough away from his car before it exploded.
Try this scenario. Say Mehmedbašić's bomb lands in the street on his side (he was sitting on the left-hand side of the rear seat) and detonates, and he loses his left leg which got mangled by the shattered door/car body. General Potoriek, who was sitting opposite the archducal couple, gets hit by the force of the blast as well and is killed, as well as the other aide sitting next to the chauffeur (can't remember his name at the moment). Sophie, being shielded by her husband and Potoriek, is not badly hurt though she's struck by several fragments and her white dress is pretty thoroughly splattered with the blood of her husband and the Governor. The Archduke is taken to the Konak - Potoriek's official residence in Sarajevo - and is saved by the quick intervention of army surgeons, though he lies close to death for several days and is unable to resume his duties as
Thronfolger (heir to the throne) and Army Inspector-General for some weeks thereafter.
I'm not sure that Franz Ferdinand would be driven into a "let's go to war" frenzy unless his adored wife had gotten killed, and fortunately, according to the OP's scenario, that doesn't happen. We do know that he had been pretty reluctant to go to Bosnia in the first place, in large part because he expected exactly such attacks as took place, and that one of the main motives for his agreeing to go was that he wanted to give Sophie a special treat for their wedding anniversary, taking her on a trip where she could get equal honors alongside him as spouse of one of the top-ranking generals in the Imperial and Royal Army instead of being forced to take a grossly subordinate role as ranking behind all the archduchesses at the Hofburg (this could get outstandingly petty sometimes; she wasn't allowed to attend state dinners with her husband, for example, but a place was still set for her and left empty!) He'd be more likely to comment on the attempted assassination with his usual darkly sardonic humor once he recovered (as he actually did, OTL, a few minutes before he and Sophie were killed; he actually told the people gathered around him at Sarajevo Town Hall that he'd be willing to bet that Mehmedbašić ended up being given a medal and appointed to the Austrian Privy Council!) The point, as a number of people have mentioned, is that he'd be unable to influence government decisions for the first critical weeks or so; by the time he was able to make his influence felt again, it'd probably be too late - war with Serbia might be a
fait accompli by then. Once he regained consciousness, he'd probably do what he could through allies such as his protégé and heir Archduke Karl, but it's uncertain whether that would be enough.
in particular if FF goes on with the idea of granting more power to the southern Slavs).
