Hhi, sandeepj1991, I think your itinerary looks great, and you will love all those places. I'm assuming you have booked all your lodging now. Are you staying in Portree on Skye? Or someplace else?
Regardless, London is fantastic. Have you looked at any guidebooks yet? There are a number of good ones from Rick Steves or Lonely Planet that have all the "must-sees" of London. I'm heading there myself and in fact, will be in London from March 19 through March 24, and have plans to see Westminster Abbey (a must for me), Tate Britain (there is an exhibit of John Singer Sargent paintings I want to see), St. Paul's Cathedral, The British Museum, The British Library, Kew Gardens, Richmond, Greenwich (and all the attractions there), Victoria & Albert Museum, Tate Modern museum, Borough Market, Southwark Cathedral and Shakespeare's Globe Theatre.
There are many other things to do as well. If you like walking in green space, there is Kensington Gardens, Kew Gardens, St. James Park, Hyde Park and much more.
Can't help you much with the Cotswolds, but was in Skye for 4 nights last year and loved it. I had a rental car, however, so that made it much easier. One suggestion you might consider as an alternative to renting a car is to do some tours while you are on Skye. One of the members here did that and posted about it. So check out this thread of his: https://community.ricksteves.com/travel-forum/scotland/skye-without-a-car
I haven't been to Shetland (yet) but I do not think 4 days is too much. I plan on staying for 7 days once I am able to get there. Here is one post that might be helpful: https://community.ricksteves.com/travel-forum/scotland/activities-on-shetland
Some good websites for Scotland are Undiscovered Scotland, which has a wealth of information about the places you are visiting, and Walk Highlands, which gives detailed information on hikes and walking in Scotland
Edinburgh is lovely as well. It's a very walkable city with a lot to see and do. If you have time (and you should), you could take a day trip to Stirling Castle, which is wonderful. This was one of my favorite places in the area and I am so glad I went. It was easy to get to, involving a quick 45 minute train ride to Stirling. The castle is gorgeous and they offer free guided tours, and there are incredible views from up there. The town of Stirling is lovely and interesting, too, with many historic buildings and a nice ambience.