We fly into Bergen in early September and will spend a couple days there, I was thinking of going on the ferry to Balestrand, stay there a day and then to Flåm. I thought we could do the Flåmbana train and then go to Oslo from Myrdal. I am worried that I am missing some fjord viewing with this plan. We will not have a car.
I believe there’s a Nærøyfjord tour out of Balestrand. That will give you a much better view and appreciation of the fjords than simply being on the Sognefjord. You’ll need to check the ferry schedule between Balestrand and Flam to ensure you can pick up the Flamsbana without needing to spend a night in Flam.
The Naeroyfjord ferries--also a key, scenic part of the Nutshell route--run between Flam and Gudvangen. They do not go to Balestrand. To get to Flam for the Flamsbana, the Naeroyfjord ferry, or both, you'll have to take the once-a-day express boat from Balestrand to Flam. That's the same boat you will have taken from Bergen to Balestrand.
I'm traveling and don't have access to my notes on the Nutshell transportation schedules, but I think you can find the boat schedules on the NorwaysBest website site. You can see the timing of the Flamsbana on the vy.no website if NorwaysBest.com doesn't have it.
I don't think it works very well to spend one night in Balestrand when you want to do the Flam-based segments of the Nutshell route, but it may work if you're willing to settle for just the Flamsbana. (Yes, you are missing something if you don't take the ferry on the Naeroyfjord.) Be sure the very limited time you'll have in Balestrand is worth the hassle. There's a reason RS recommends staying in Balestrand only if you have at least two nights available.
I apologize, acraven is correct. It's not the Naeroyfjord, it's the Esefjord with Balestrand Adventures, https://www.balestrandadventure.no/. They do offer private trips which might include the Naeroyfjord but I assume that would be pricey.