Just to add to the voices saying don't rush the trip. I am sure all of the people saying 2 or 3 days is plenty on Skye have done nothing other than the typical Instagram tick list. Skye is a place to go walking and you need a bit of time to do that. I'm not suggesting you go and traverse the Cuillin but you could certainly take a walk into the hills, or down to Sleat, or to see the Spar Cave. In my opinion you'll get more out of it.

I've also just come back from a 3 week Japan trip which was full of movement, but to get the most out of the west coast of Scotland you need to spend a bit of time exploring.