I'm not all that familiar with the war, but from what I've read on here, perhaps killing off some critical Roman leaders early on might tilt the balance... say, Fabius, Marcellus, the younger Scipio?
It is always going to be hard to say for sure but probably not. It has been suggested, by Livy I believe, that the 2nd Punic War was Hannibals individual genius pitted against Rome's corporate genius. For example the strategy that saw Scipio landed in Africa had actually been decided on before the war began...only Hannibal running about in Italy delayed things and the elder Scipios made sure it did not delay the Spanish endeavour.
Fabius obviously gives his name to an entire brand of military-political thinking but again it is likely he was appointed dictator more because he represented the strategy agreed upon by the majority of the Senate. It is worth noting this was seen as the sensible course of action even by Hiero II off Syracuse who himself sent a suggestion along those lines to Rome.
Marcellus is perhaps the most likely to cause an upset even though he was the one who did in actual events manage to die like a pillock however the loss of Nola is probably the worst result likely to be produced by him deciding on a bit of dodgy personal recon even earlier and again I cannot see that ultimately changing much.
I think having read up in as much detail as I can manage the last few days Hannibal's best chance of doing something decisive would have been to take Tarentum (most likely though another good sized port would do) abandon efforts in Italy and try in Sicily. Then again even here Hannibal's truly abysmal record in siege warfare does not presuppose total victory on even just that island.
However maybe if he could win well enough to preserve New Carthage and the Punic position in Spain and perhaps cement the transfer of Syracuse into the Carthagian sphere that might for a much more interesting 3rd War or even (unlikely I suspect) a prolonged period of relatively peaceful competition.