Edinburgh to Skye is a full day of travel - and then you have to get back, presumably to London? Luskentyre is a huge journey, even if you flew to Stornoway you'd land way off.
Beach in Scotland is not rare. Lounging in the sun in September is, even if it is sunny it will be pleasant rather than hot.
Start in Inverness. Direct from London there are 2 sensible options and both may be selling out already.
Overnight train in sleeping car (private 2 bunk compartment in Standard class). https://www.sleeper.scot does not run on Saturday nights but reservation system is stupid enough to let you ask. Runs from London Euston station in central London. Also has sleeping cars that go direct to Fort William on west coast which is also worth considering. Seats are not worth considering. Travel to Scotland is always dearest on Fridays and cheaper Tues/Wednesdays. At present from £110 each but by end of week £150 is more likely and in two weeks could be £200. But saves a night in a hotel so deduct that and gives you more time to do what you went for, which must have some value.
Fly. Two airlines, 3 London airports, an hour or so in the air (obviously much more on the ground!!). BA go from Heathrow, mainly for the connecting passengers, Easyjet go from Luton, these are usually both after breakfast and land around 11:00. Easyjet also go from Gatwick at lunchtime and land mid afternoon. Flight prices are cheaper than the Sleeping Car BUT you still have to pay for the previous night hotel, the cost of reaching the airport, luggage (with easyjet) and you lose at least half a day in Scotland.
https://www.easyjet.com or https://www.britishairways.com
Inverness is the capital of the Highlands. You can move on to Skye from here (if you go overnight you could be there for lunch). From Skye take the ferry to Mallaig and come back towards Edinburgh via Glasgow.
https://www.scotrail.co.uk/
