In the Alps there is a dense network of huts mostly maintained by the local alpine clubs. There are also some private huts mostly owned by mountain guide associations.
Most of the huts are closing down towards the end of September but many have winter rooms or small bivy huts that are accessible for the whole year. Especially Italy has a lot of bivy huts ...
https://www.outdooractive.com has a lot of skitour trails in the Alps, and at least a few in the area you mentioned. AFAIK, they share their database with www.alpenvereinaktiv.com, which is actively supported by the german alpine club.
I think you're going to have problems with camping.
The age of responsibility in Italian law is 18 years.
I've looked at the terms and conditions of a number of campsites, and they all say that each group must have at least one responsible adult.
I suspect that this will vary from site to site depending on their insurance etc, but on a quick search I was ...
In the region managed by CAI Vigezzo, there are actually many bivaccos (unstaffed shelters) that are open year round. As most of those were not on either the Swiss topographic map, or Openstreetmap, or online sources I consulted prior to departure, I will list them here. During my hike 2019-10-25/28, I passed by:
Alpe Croso Fuori, OPEN, basic
I seem to remember being told that Italian huts will have an emergency shelter room as well.
In any case, this emergency shelter may not be meant for people who stay there over night during a planned trip: it is meant for proper emergencies.
I've seen signs saying "to stay while not staffed, please contact (phone number of someone from the local CAI ...
According to the Italian language Grande Traversate delle Alpi, Vol. 2, the GTA continues to the Lago Maggiore, which (unlike any other description I've seen) would be consistent with the photo I took above the Val Agrasino. According to a review of this book, the northern/eastern end would be Cannobio at the Lago Maggiore.
All over the Alps the huts and bivouacs can be divided into:
available to anyone when unstaffed (some require key and registration, some not)
available only in emergency when unstaffed
open all year round
You have to check each one individually.
For huts on the Swiss side, Swiss Alpine Club website provides all the information: