+1 to the 9:51 poster. We were there a few years ago and Skye was a bit of a zoo. Getting across the bridge into Skye took forever, parking at Old Man of Storr or the Quirang was a mess, and there were traffic jams everywhere out of Portree. The Highlands (Oban, Glencoe etc.) were less crowded though, but yes you would bump elbows on most hikes. The trouble with getting up early was that most of the interesting spots were still foggy and wet. Admittedly, seeing a ghostly Old Man of Storr is quite an experience but I would not say the same for hiking the Quirang in fog.
Check out
https://www.walkhighlands.co.uk/skye/ for some nice walks. The Trotternish is highly recommended.
That said, we did not have to book lodging more than a couple of months in advance.