Pompeii and positano

Pompeii would be very simple and inexpensive as a DIY
take a cab to Napoli Centrale then Circumvesuviana to Pompeii
There are tour guides at entrance or consider meeting up with a Mondo Guide group
Www.sharedtours.com
( assuming you are docked in Naples?)

Positano is not a good fit on the same day, if that’s what you had in mind
I suppose you could take ferry from Naples to Positano

Another option is to hire your own driver for the day to take you both places and wait while you visit
Here is one company, there are others

https://www.topexcursionsorrento.com/?portal_referer_id=46

I believe RS has a guidebook for cruisers with DIY excursion suggestions
https://store.ricksteves.com/shop/p/mediterranean-cruise-ports

Where does the ship stop and for how long?

I am not a cruise traveler, and have no personal experience related to this. But, I have often read on this RS Forum that if an official cruise ship excursion group might be delayed in traffic, flat tire, etc., the ship will wait to depart. But if passengers are doing their own thing and are late, the ship will NOT wait. So, smart to not cut your schedule too close. I hope others might be able to write about this from personal experience.

We found a tour in 2014 of Pompeii and the Amalfi Coast through Viator for about half the cost of what the cruise ship was offering. However, a friendly warning that you might be so rushed that you'll see a little of both but not enough of either. I'd choose one.

We paid the $ to cruise for our Pompeii stop, but did a 1/2 day tour vs a full day which had other sites included like you seem to want. It meant I did not have to worry or concern myself with details, we had built in guides, and we had a great day. The extra was worthwhile as if there had been a problem and ship is able- they will wait for tours. We had one situation come up another tour group had bus issues and we waited. Had we been unable to wait for them the cruise would have paid their hotel, dinner, and to get them to next port.

Everyone has their own comfort zone and peace of mind when traveling and what value to place on things of course. No wrong way just sharing what we did and why.

OP, you neglected to mention which port you will dock at ( we are assuming it's Naples), and most importantly when the ship will arrive and depart. Again, we are assuming the ship is not remaining over night.

As previously noted, Pompeii can easily be done independently. Positano could be easily (but not cheaply) done with a private car hire, or done in a more complicated and risky manner with a combo of taxi, train and bus or ferry . But the further from the ship that you travel, the greater the risk of missing the ship if not on a ship excursion. I'm all for independent touring on cruises, but we don't risk it if it involves travelling far.

And finally, trying to do this in combination on a port day, is a recipe for disappointment. You'll only be left with hours spent getting from place to place, and only the briefest of glimpses of either place. Pick one or the other; not both.

You might have a look at Cruise Critic. There is a Ports of Call forum that will have more advice from cruisers' perspectives. Also look up your Roll Call for the ship you are sailing on. There may be fellow cruisers who are setting up a private excursion you could join.

My first experiences in Italy were via a cruise and our first port of call was Naples. Pompeii was a priority to me, but my wife was more interested in the Amalfi coast. We found a shore excursion on Viator which picked us up at the pier, drove us to Pompeii where we had a 2 hour tour. From there we went to a local restaurant for some pizza and then on to Sorrento for 2+ hours on our own to explore. While Sorrento isn't the Amalfi coast, it is beautiful and a good alternative to Positano with the time constraints that come with cruising.

As an alternative, many tour companies let you set up a private tour, which you can "advertise" with others on your cruise via a forum (I used cruise critic with great success on a tour I set up out of Livorno). The benefits of this approach are that you determine how many people are on the tour (and thus the cost, which was about half of the ship's shore excursion) and exactly where and for how long you want to visit.