In 2024 we took the Cinderella II Stromma boat from Stockholm to Vaxholm. We loved the view of the archipelago from the upper deck. It was a 50 minute boat ride to Vaxholm with 2 stops. We purchased one way tickets in advance for a certain time. Some passengers on the Cinderella II were going on to other places in the archipelago. Vaxholm was very charming and we enjoyed it.
Returning to Stockholm from Vaxholm we took the Waxholmbolaget boat, an older wooden boat. We took whatever boat was going to Stockholm when we wanted to depart and paid on board and showed our ticket when we disembarked in Stockholm.
We did not research any private boat operators, so I cannot speak to that. The Stromma Cinderella II boat was great.