you should think of reaching Sicily on a separate ticket, be it a miles ticket on IB/BA/LH or simply buy an LCC ticket like Ryanair or EasyJet.
Check the CAT and PMO airports Wickipedia page to see which airlines serve those airports from where. Then map out your options.
Bear in mind, many of those flights are seasonal, meaning it probably stops after Mid Sept.
Also be sure to check Italian government's website on Public Transportation Strikes Announcement. It is required by law that ANY public transport entity, be it a big city or a small town, air or land, if the unions plan a strike, it has to be announced ahead of time and the schedule posted on the government website.
Why did I know this? Because in our 2018 trip to Sicily, our flight from CAT to MXP to catch the next day AA back to US, was canceled 36 hours ago. When I checked google flights, ZERO direct flight available on that day out from either CAT or PMO to MXP or FCO. The day before was all sold out. Apparently others knew the strike was coming and planned ahead to book the day before flights to leave Sicily to Italy Mainland already. The only option to get to MXP was via CDG if I must get to MXP on a single journey...
Google flights are very intelligent. After I spent over an hour frantically searching for options, it popped up to suggest flying to Turin... We actually had been in Turin a few years ago and took the 1.5 hr train to MXP after a few days. But in the panic moment I totally forgot about this possibility!
So I was able to grab the last flight a day before from Catania to Turin on AZ. Then the following day we took the train to MXP for the next morning 10am AA flight back to US.
Upon returning home I decided to find out what was going on that day why both FCO and MXP seemingly closed. It was caused by Italian Air Controllers Planned Strike! The only blog site I found this news had the link of the Italian government site for all public transport strike news. Unfortunately I dont find it in my file folders now. Though I guess you could google and find it.
The thing that irked me a lot was, the strike was a known event, long been announced, yet the airlines still sold the tickets of the flights on the strike day... WITHOUT any notice.
Ryanair refunded the tickets via online chat when I tried to file EU240. No EU240 compensation due to the disruption was caused by airport strike but full refund was due.
Chase reimbursed the hotel nights lost due to schedule changes, also because airport strike was a covered event. But the new tickets to Turin were not covered as those were new expenses, according to the insurance T&Cs.