9 day itinerary for late September advice

You have chosen very popular islands to visit. All are good. However you have not taken into consideration the time required to make a ferry hop from one Island to another. You should be aware even a short hop is going to take up half a day because of the ferry time tables. So your plan will give you about a day and a half for each island. Your hotels are going to want you to check out at noon at the latest so you are going to spend lots of time at the ferry ports just waiting for a ferry.
Logistics are important when ferry hopping.
Here is something to consider.
I would suggest you get to Naxos. There are excursion boats to Mykonos with a bonus stop at the ancient site at Delos. Return to Naxos in the late afternoon.
You can also take an excursion to boat to Santorini and back to Naxos in the late afternoon.
I would choose to go to Naxos and just stay there for a few days. At least that plan gives you time to relax and enjoy Naxos .. Honestly you need a week in Naxos just to experience some of it.
By the way, itinerary 2 has one less island hop which makes the logistics better than option 1.
Slow down your time is limited do not waste precious time ferry hopping each day.
Here is why Naxos has it all.
https://www.flickr.com/photos/stanbr54/albums/72177720334044112/
https://www.flickr.com/photos/stanbr54/albums/72177720329571437/

If you're going to party with your friend(s), go to Mykonos and stay there. The island is made for that, and practically 365 days a year, 24/7.

https://youtu.be/dMpaksY4sTE

https://youtu.be/wegUM2i5eRI

Obviously, you will need to account for the budget that goes with it. Mykonos is one of the most expensive places in Europe.

Why would you want to waste your time on ferry trips, especially since you are planning to stay on each island for a very short time? As stanbr explained, you shouldn't measure by distance, but rather by ferry schedules and transfer times, which take at least half a day for every move from one island to another.

Santorini isn't necessarily interesting in terms of culture (except for Akrotiri) and partying (although there are quite a few cocktail bars with DJs in Fira). It is primarily for its landscapes and perhaps its wineries.

Naxos is too big an island to suit your plans.