In 2016, I did a similar journey, without a car. My connections were well-timed with little waiting. There were no long ferry rides. There was one flight.
I took the train from Edinburgh to Thurso. I loved every minute. The route is definitely stunning.
I shared a taxi from the Thurso train station to Scrabster where I spent the night. The other person went on to her ferry.
The next morning, I had a longer than expected walk from my little inn to the correct ferry. My ferry went to Stromness. That ride was fun.
The local bus arrived shortly after the ferry's arrival. I took it to Kirkwall. I was the only person on it. I'm guessing that's because most people rent cars.
Being a slow solo traveler, I spent 4 nights in Kirkwall.
One day I went on a very reasonable day tour of the main things to see. I set that up with the TI next to the bus station. I was the only person on it, but was not charged extra. That was my busiest day.
One day I did maintenance activities. You know, like laundry, resting and watching some challenging weather from my comfy room.
And one day I nosed around town, doing and enjoying things most people probably don't and purchasing a silver ring with very primitive runes. I've worn that ring almost daily since I bought it and I'm wearing it right now.
When it was time to leave, I took the local bus from Kirkwall to the Kirkwall Airport. I
flew from there to Aberdeen.
If I were to do it again, I'd make only one change. I'd spend the night in Thurso and have a taxi take me as close to the ferry as they could.