Unless the coat is light weight you may not need it, but will it be cold? Yes, probably very cold. We did Alaska in late May and it was cold and rainy most of the time. As Ute-Fan said, layers is the way to go. Now, as for bad reviews on NCL and the Pearl, I don't know where you are reading the bad reviews? You can always find some, regardless of the ship or the line, but many would rather cruise NCL than any other line and the Pearl is close to brand new with very favorable reviews most of the time.
Because of freestyle and a few other things, NCL is a little different from many lines, but this is not a bad thing, just different. I think those who write negative reviews were not prepared for the particular experience, or are inclined to nit pick. There will always be those out there as well.
We have cruised all mass marketed lines, each has a nitch and cons as well as pros, but for us, NCL comes the closest to fitting our life style.
My recommendation for Skagway, do a private tour on a van. I am sure there are many companies that do this, I can't remember the name of the one we used, but it was one of the best tours we have done (that is saying a lot cause we have done a lot) Check the roll call section on CruiseMates and as much as I hate to suggest another website, try the rollcall or ports a call site on CruiseCritic as well. You will get lots of great ideas.
Now, as for the inside cabin, well, this might be the one thing that be a little different for you. We have only done inside once and I do not think we would again. Actually I am trying to talk DH is doing the Spirit in November and opting for inside, he just looks at me and wonders what drug I am on. this doesn't mean your cruise will be spoiled, it just means you may have to take a deep breath and remember you used your Time Share points.