Sounds great.
One night is probably enough for Glencoe unless you are intending to spend a full day walking in the area. Think about adding the night saved to Skye.
Skye - even for October, it makes sense to get accommodation booked well in advance as it is very popular with visitors.
I’m a bit confused by the Blackhouse village - is this the one that is part of the Highlands Folk Museum , or is it somewhere else? (The only other one I can think of is Gearrannan which is Isle of Lewis... )
On your way from Skye to Inverness, think about doing a detour to Glen Affric. This is one of the prettier glens but not on the usual tick list. There are two easy and very pretty walks you can do - Dog Falls and Plodda Falls with an impressive viewing platform above the falls.
Next day do Culloden, Clava Cairns and Fort George. Clava Cairns are open 24 hours. These are best seen early morning or late afternoon when the light is low. They are much more atmospheric then! If you have time, visit Clava Cairns before Culloden, which opens at 9am. Failing that, visit them after Fort George.
There is a lot to see and do in the exhibition in Culloden Visitor centre. If they are running the guided tours of the battlefield, it is definitely worth joining one. They give a very good summary of the lead up to the battle and why it went so disastrously wrong for the Jacobites. Fort Geoge is about 30 minute drive, This closes at 4pm and there is so much to see, so you need to be there by 1pm...
Next day head to Highland Folk Museum. Allow just over an hour to drive there. It opens at 10.30. Again allow plenty of time to visit as there are a lot of buildings to go in. I spent just under three hours there and could have done with a bit longer...
Then drive down through Cairngorms to Pitlochry and visit the Enchanted forest. There are timed ticket slots from 17.30 until 21.00. Sunset will be around 6.15, so choose a time after 19.00 once it is dark. I’ve not done this one but have enjoyed similar elsewhere. Reviews on Trip Advisor are very positive.
Then spend the night in Pitlochry.
Have you come across the Undiscovered Scotland website? It is a wonderful source of ideas of places to visit and things to do. It contains many hidden gems which don’t feature in the guide books. Start with the relevant map page and follow the links to text pages with information and lots of pictures.