Hi Shiennart -
I've done the West Highland Way and hiked on Skye. If you are planning on using public transport then the West Highland Way seems to me to be your best bet, given that I don't believe there are too many options on Skye in terms of public transport. Also I'm not sure that there are too many 'trails' on Skye other than the Trotternish Ridge walk, which I haven't done (and I'm prepared to be howled down by others who will tell me there are plenty of point to point trails on Skye!).
I would suggest that most people who walk on Skye will be into ticking off peaks in the Cuillins and the Black Cuillins in particular and these are not easy strolls, but challenging hiking in very rugged country. I for one was happy to be in parties who were carrying, and experienced with, ropes and the accompanying paraphernalia (helmets, harnesses, etc., etc.).
The West Highland Way is a national trail and is designed for the walker only, although given that it takes a largely low level route, it's not to be taken lightly. If you need to do something that gets your hands out of your pockets there are plenty of of side trips you can do - we took several options to go up peaks after we'd completed a section or during the course of a section and, of course, we left a day at the end to scale Ben Nevis. The WHW does cover remote country especially as it gets further north, but you at least have more transport and accommodation options near or on the route than Skye might be able to offer.
That's not to say Skye is without merit, it is, in good weather, absolutely sensational. But the above is correct - you can't go far wrong with any walking in Scotland.
Whichever you decide to go for, have a great trip!