We have sailed out of Skye a few times as well as sailing up both coasts. We have always launched at Millivaig near Glendale which has the most amazing cafe/cakeshop (keeps the crew happy). I’m almost positive you would be able to launch at Broadford and now that the ferry no longer runs the slip at Kyleleakin would be brilliant as well as giving a very sheltered harbour. I also recall a usable slip/ beach at Isle Ornsay down the Sleat penisular. I don’t know about Elgol but most of the little sheltered places on the coast have some kind of access of Wayfarer size boats. Soay just off Elgol has a really well sheltered harbour and well worth the visit, even if it is just to see the solar powered telephone exchange!! From the Broadford side The Crowlins are well worth a visit but I would only plan to sail through them on a spring tide and following wind. You could also get to them from Plockton although a bit longer sail. Plockton is really well sheltered and an easy launch/recovery but the village is very restrictive on leaving cars/trailer especially at the tourist season.
Hope this is of some use
Iain Mc Robbie