I have asked the Gruppo Guide Etna Sud, which is an official guide group which is responsible for organizing excursions to Etna and supervision over the tourists. Although it took some time to explain that we really want to hike on our own, we have finally received an answer:
Hello,
our cabin is open from 08.30.
You can join Torre del filosofo being at 10.30 already there and booking a few days before.
The cost would be € 30.00 per person.
We have also asked when their cabin is being opened, as we need to rent some equipment. As we can see, it is not possible to rent equipment and hike on one own in two hours.
I will expand the answer basing on final experience and what happens in September.
We have hiked the Etna on our own, but only up to 2700 m a.s.l. due to the recent activity. Therefore we were not able to reach the summit. However, we were reassured that in general it is possible to use the guide only for the final part (from Torre del Filosofo to the summit). It has to be arranged with them in advance.
Hiking Etna up to 2700m was exhausting for us and we think we wouldn’t have managed to reach Torre del Filosofo on time and have enough energy for the summits. Still, there is an option to use the cable car only (it is the most exhausting part) and then reach Torre del Filosofo from the cable car station, it is quite manageable.
My wife and me had actually the same question around ~10 years ago when going to Mount Etna. When I remember correctly, use of the cable car as well as a guide was mandatory for going upwards (but they let us walk down on our own).
Not sure how the regulations are today, I guess your best bet is to contact a guide bureau (like this one) by phone or email and ask them directly.
Stromboli was also interesting, we had a visit during the same holidays, but they definitely forbid any private people to enter the top area without a guide, with severe penalties when they catch you.
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