Hi Liming,
There isn't an official (or otherwise) coast path around Skye. There are plenty of sections of coast that give a great walk, most of which are on this site, but there are no signposts etc. and to walk continuously round the coast you'd need to be backpacking as some sections are very remote.
If this doesn't put you off, I'd recommend the book 'Skye 360' - available under Skye walking books in our bookshop. This is the story of one person's walk right round the coast, and would give you the best idea of what it would be like.
If you are looking for an official coast path - I'm afraid there isn't one in the West Highlands - though there should be
The only multi-day coast paths I'm aware of in Scotland are on the Moray Coast, round the coast of Fife and also parts of the Lothian Coast (John Muir way).
Good luck, whatever you decide.