We are going on the Norwegian Iceland Fjords cruise in July. First time going on a
Disney Cruise. Do you have suggestions regarding the shore excursions? Do you do any from Disney, or did you explore on your own? I am now in the process of figuring out what there is to do and see at each port. We have 2 kids, ages 6 and 10 at the time of the cruise. Would love to hear your experience!
We were on last summer's sailing of this itinerary. I'm not sure off hand if your ports are exactly the same as ours, but here is what we did. Keep in mind, our son is quite a bit older than your children (17).
Oslo - We hired a private guide, but still used public transportation (and our feet!) for transportation.
http://www.guideservice.no/no/ Having the guide was not essential - but it did offer a nice addition to the sights we were seeing and wasn't very expensive as it did not include transportation. Oslo is very doable on your own and the public transportation system is great. I would not pay Disney prices for an excursion here. The Viking museum is terrific, as is the Folk museum. We also visited the Fram museum which is worth a peek if you have the time. We walked around the fort but could not go in as there was some kind of event that included the king, and pretty much everyone else in power at the time we were there. We did get to see the king's guards and his car, though

. The Norwegian resistance museum was just fascinating. My son who is a history buff was in heaven. He spent more money in that gift shop than anywhere else on our trip - all books! I'm not sure about younger kids, though.
Kristiansand - I really couldn't find much that interested us here, so we took a short Disney excursion. It went to a small fishing village (charming, but not a lot there) and a folk museum. The folk museum was nice, but paled in comparison to Oslo's. We were back on the ship in time for lunch and spent the afternoon at the spa.
Stavenger - We did the Lysefjord cruise through Disney. It is cheaper if you can book it independently, but we had a very short time in port and the timing just didn't work with the Rodne boats. So we did Disney and it was beautiful - highly recommended, though again not sure if younger children would be bored. If the timing does work with the Rodne boats they are literally steps away from where the Magic docks. I'd go that route in a heartbeat over Disney.
Reykjavik -
www.discover.is - I cannot recommend this company enough. We spent both days with them, touring the area in their super jeeps. It was amazing. We did the Golden Circle tour - including going out on the glacier (a highlight of the day!!) and the Reykjanes Peninsula and Blue Lagoon tour. Both were fabulous and the guides were terrific. My son loved this so much, he wants to spend his summer breaks from college driving jeeps in Iceland (hopefully he changes his mind

). While your children are younger, I can tell you without a doubt my son would have loved this at any age. But then he was hiking in Yellowstone at age 3. YMMV.
Akureyri -
http://www.inspiration-iceland.com - Another great day. This was supposed to be another super jeep tour, but there was a mechanical problem with the jeep and we used a van instead. That was a slight disappointment to my son, but it didn't end up detracting from the day.
Kirkwall - We used
http://www.orkneyaspects.co.uk - Wow is all I can say about this day - amazing sights, beautiful island - we even got to go inside a 5,000 year old tomb. Though, unfortunately, I would say your chance of booking with them at this late date is about zero. Kirkwall is tiny and there aren't that many tour businesses. But take a look at their website anyway. That should give you an idea of the highlights.
You didn't ask about Copenhagen, but try to spend as much time there ahead of time as possible. It's an absolutely beautiful city and so easy to explore on foot. We came in three days early and weren't ready to leave when the time came to board the ship.
As for Disney vs private guides. Everyone has there own comfort zone. All I can tell you is that each and every guide we used was completely focused on insuring we arrived back in time. They usually shoot for about an hour ahead of time, to allow for the unexpected. Remember that in this day and age of instant online reviews, just one instance of causing someone to miss the ship could devastate their business. If you do you due diligence - I poured over Trip Advisor, this website and Cruise Critic - you should be fine. In most cases, we paid about the same, or less, for a private guide for just our family as we would have to be crammed on a bus with 40 or 50 other people. Our guides were also quite funny in how they did everything in their power to avoid those buses. While at times it was inevitable that we would catch up with the crowds, we often had sights completely to ourselves or with just a handful of other people. At each port we were back on the ship, sitting on our balcony drinking a glass of wine while we watched all of the last minute folks pour in. But again, everyone has their own comfort level with this. This was our first time venturing outside of the Disney bubble and we loved going that route so much that for our next cruise (Canadian Coastline) we have already booked our excursions and both are independent of Disney.
Have a great cruise. Whatever you decide it will be wonderful. You really can't go wrong in those ports!