Itinerary help- Scotland with no car

Oban is a place most folks seems to use as a base for seeing Mull/Iona/Staffa. There's also the smaller island of Kerrera right offshore, which reportedly has a nice walk. If you don't have plans of that type for your full day in Oban, it's possible some other location would be better for you.

On my first trip to Scotland, I did 3 weeks solo without a car. Pretty similar to your route. I used tour to get over to Skye. My only hiccup was trying to see Glencoe. The bus I was on did not actually go into the small town of Glencoe but dropped me off in Ballachulish. I walked into Glencoe. I tried to schedule a bus to go through the glen and the buses were full as were all the taxis. So, on my first trip I did not actually see the scenic drive. I would make sure you know your bus routes ahead of time. This was in 2017 so things may have changed. I remember that being a regret of my first trip. You will love it in May all the bluebells!

From Inverness you would have to change buses for Glencoe at Fort William. Depending where you choose to stay you may find it easier to take the local citybus #N44 from Fort William.
The same for Oban- take the N44 or walk or taxi? to Ballachulish then pick up the Oban bus from there.

Bear in mind that coming from Inverness and going to Oban, staying in Glencoe Village you miss the drive through the Glen. To do that you need to bus from Inverness to Fort William, then switch to a Glasgow bound bus as far as Bridge of Orchy, then bus back down the Glen to Glencoe Village.
Depending on how the buses are timed it may be best to stay on to the larger village of Tyndrum, to turn round there, Bridge of Orchy is a bit of a "blink and you miss it" place.

Apart from Kerrera the other great close by island for walking is Lismore. That ferry leaves from Oban ferry terminal. The boat to Kerrera leaves from a slipway almost 3 miles out of town.

The train from Oban to London- you either switch twice- at Glasgow Queen Street and Edinburgh- to Kings Cross. Or change stations in Glasgow using the free #398 bus then train straight to Euston from Glasgow Central.

Re- The above- going from Fort William to Tyndrum and back. If you look on the current winter timetable that might look hard. But looking back at last year's summer timetable (of which I have a paper copy) it works on the 11110, 1310, 1510 and 1740 buses from Fort William- on the 1740 you have to change back at B of O as there isn't time to get down to Tyndrum for the change back.

This is a video of the very scenic Fort William to Oban bus route (the Glasgow bus takes the same route as far as Ballachulish)-

https://www.youtube.com/watch?v=hl2XyQIqjRo