Nobody really knows what will happen, most likely AZ will have lots of strikes and disrupted service but not cease operation. Your flights may be delayed a day or 2 or 3, but will eventually get there. Ground staff striking is likely to delay other airlines into Italy as well as AZ, you may wind up having to fly to ZRH or some other non-Italian airport and take the train. But the disruptions will probably affect 3 or 4 days in the month and things will be normal the rest of the time, so it is a matter of luck which days are picked. There isn't any sure way to avoid it except to avoid going to Italy. The DL issued ticket has a bit more protection, but in theory Skyteam will help you even with the AZ issued ticket (they have no legal obligation but would almost certainly honour AZ tickets even if they become worthless).

As for having a paper ticket instead of an e-ticket, the big advantage is that it is easier to go to another airline and reroute with a paper ticket. Given the possible chaos at AZ (including strkes by the computer workers, maybe having the e-tickets inaccessible while the computers are down) it would be wise to have paper tickets in this instance. The worst case scenario is that AZ suffers from some industrial sabotage and their computers are down for a month (and your e-ticket disappears until they recover). Very unlikely, but not unprecedented in Italian labour disputes.