I have to agree with Anaxagoras, an important butterfly like that is bound to cause the specific Battle of Hattin to be different. IIRC Guy led his army across the desert when he could have waited for Saladin to do the same, even that would have serious consequences.
What I wonder is what was Byzantium doing in those years? How would Stephen go deal with Manny K?
He did. And assuming the same siege, why would Stephen necessarily do differently? (We can say "Stephen is a better king than Guy" and able to control the hawks, but "Stephen is different than Guy, therefore things go differently purely because he's not-Guy" is unconvincing).
Its certainly possible - but this "butterflies would do it" is giving them the power to change events on their own that I find very implausible.
When is Stephen becoming king, in this scenario?
Baldwin (IV) is still born, is still alive, still the heir (unless the barons decide to go for elective monarchy and no one supports the poor guy) and there's no particular reason his leporsy is going to be worse than OTL.
Wondering since if he becomes king at the same time as Guy did OTL, Manny K (which is a less jarring image than Johnny K, if still weird for a Byzantine emperor