Hi, Giangilberto from Milan, Interbus connects Catania Airport to Syracuse without passing through the city center. The journey takes about an hour and fifteen minutes; buses depart every half hour from just outside the arrivals terminal. Here is the link to the Interbus website:
https://www.interbus.it/
This is the best option, as taking the train would require you to first get to the Catania Centrale station.
Regarding your fear of driving: your concern may be valid, but, in my opinion, for the wrong reason. The problem isn't Sicilian traffic itself, but rather the fact that Ortigia has a ZTL (Limited Traffic Zone); the island is almost entirely pedestrianized or restricted to limited traffic. Below are the official regulations from the Municipality of Syracuse website:
The Limited Traffic Zone (ZTL) in the historic center of Ortigia is in place to regulate access for unauthorized vehicles, aiming to preserve the area's historical and artistic heritage while improving livability and urban safety.
ZTL Activation Times
Type of Day | Active Time Slots (Access Prohibited)
Weekdays (Monday to Saturday)
11:00 AM – 3:30 PM
5:00 PM – 2:00 AM (the following day)
Sundays and Public Holidays
10:00 AM – 2:00 AM (the following day) (Continuous coverage)
If you arrived by car, you wouldn't know where to park it, unless you decided to leave it outside the island.
My advice is this: you don't need a car in Ortigia. It is an island measuring one kilometer by five hundred meters, and you can get around the whole place on foot.