For some reason, I didn't see the 8/24 option when I did the search, oops. (Maybe it's sold out).
I did enough walking around in Fairbanks when we arrived that I was happy to spend the evening in the hotel, so I can't help you there (it was HOT for most of my tour, the last thing I expected in Alaska -- hot enough to be tiring).
In Dawson City, we had some out-of-town excursions built into the tour, so I spent my free time mostly walking the streets and visiting local attractioms (there's an online Dawson City Visitor Information Center that you might want to take a look at). But I'm a history buff, so the city and its landmarks were just what I wanted.
That is a pretty packed day from Dawson City to Skagway. There's only one flight from Dawson City to Whitehorse that day (10:30 - 11:40), so it's a good bet that you'll be on it. The trip from Whitehorse to Skagway is, in theory, about two hours, but you'll likely make a few stops on the way, so maybe three. And then the train trip takes about 2 1/2 hours. So you might have an hour in Skagway thanks to the "extra" hour. Most of the historical sights are along the one main street or within a block of ot, so you can expect to see them anyway!