Norwegian Cruise July 2019 Docking in Stockholm

The Vasa museum, Abba museum and Skansen are all on the same island within walking distance of each other. Gamla stan is a short tram or boat ride away, the boat also gives you a nice view of the city from the water.

The best and most efficient way depends on where you dock.

They are all located on Djurgarden, an island that originally was the Royal Hunting Grounds.
The open air, old Swedish village is called Skansen.
Vasa is number one to see on your list. There is a little ferry that goes over to Gamla Stan, old town.

As long as you have money for a taxi if you get tired. Vasa is big but walkable. Obviously, Skaagen is outdoors and requires a lot of walking to see everything, but you seem to know your limits. You know you must be back to ship on time, so allow for traffic and unexpected delays.

Not sure what you mean by tour. The ship's excursions will have a guide everywhere, but you want to do it on your own, which is very reasonable for Stockholm. I don't remember if Skaagen offers institutional tours or not. We had a free house-guide at Vasa, who was charming, did not book. But that was some time ago. Haven't been to the Abba museum! But I did see the Broadway musical.

When I was in Stockholm on a rainy day in 2017, I used tram #7 (really a bus) to move around Djurgården sites. Perhaps check to see if it’s stll running.
If you’re more interested in palaces and such, royal sites are nicely clustered in Gamla Stan for a short visit.

The tram is still running and is very much a tram.

I took the tram today !! (And à couple of other times in the past three days)