I have some ideas on this myself. First avoid the weakening of the Byzantine Empire before the Arabs attacked the empire. In order to do this, Maurice would have to keep the throne and Phocas would not be able to come to power. Hence one would avoid the Byzantine-Sassanid wars that weakened both the empires. Egypt would then secede at some time after the Arabs attempt to conquer Syria had been crushed. Probably the best would be that also the Sassanids survived, as a surviving Sassanid Empire would probably be less dangerous than a Persia dominated by the Arabs (as they had a new ideology - Islam - that would unite them). I would assume that even if the Byzantine Empire managed to keep the Arabs out of Syria, the different religious views of the areas of the empire would lead to attempts to break away. If so, what would be the most optimistic, but not ASB, scenario for Egypt?