Support with Scotland Itinerary - No Car

This sounds a very reasonable and logical itinerary well spaced, but you will need to start looking like last month for somewhere to stay on Skye.
I'm not sure what you mean by bus and West Highland Way in a day on the way to Portree.
That is a full day bus journey (change bus at Glasgow). You will see the general scenery of the WHW but precious little except glimpses of the WHW itself. You MAY just have time in Fort William to run down the main street to see the Triumphal arch marking the end of the WHW, but not much more. You are not passing the start at Milngavie and on the wrong side of Loch Lomond.
For transfer to Orkney take the mid morning train from Inverness then you have several hours in Thurso to wander down to the Ferry Terminal at Scrabster. The afternoon train is a tight connection, unless you have a taxi pre-booked and confirmed in writing from the station so give yourself time to look at the town. If going up in the afternoon I would say to use the X99 bus as that takes you straight to the ferry terminal. Northlink recognise it as a connection, so would normally wait if the bus was late.
I'm not sure if you know how far Smoo Cave is from Thurso in drivetime rather than physical miles. That deserves a full day. Fitting that, and Whaligoe steps (in the opposite direction) in (or Dunnet Head/John O'Groat) is stretching it, especially so early in the year. But a car is the only way to get to Smoo.
On your last night on Orkney think about having that on board ship. You can book bed and breakfast on the Hamnavoe (the ship) so don't have the very early start next morning to board her. Boarding is from 9pm onwards. If you can- arrange for the car pick up at Scrabster Ferry Terminal to save valuable time.
At least you'll be rested before driving, and on a fairly quiet road, all of which is good
I'm sure Skyegirl on this forum will give you some local advice about your time on Skye.

Thank you for the response!

I am considering just biting the bullet and getting some kind of tour, either from Edinburgh or Inverness for Skye. Not ideal having to sit with strangers for hours, but I also don’t see any alternative for time or sense.

If anyone can recommend a good tour where I can see Skye and some of that side of the country with reasonable stops with some chance for alone time at each place, I would really appreciate it!

Check out Rabbies tours. They are highly recommended.

Jessie, I echo Skyegirl’s suggestion of Rabbies tours. I enjoyed two tours by Rabbies during my solo trip last September. One day tour out of Inverness to Culloden, Clava Cairns and Glen Afric and a 4 day tour out of Edinburgh of the Western Highlands and Isle of Skye. Have fun exploring their site

https://www.rabbies.com/en

Jessie, I see that the visitors center for Culloden is closed every Monday in the month of March. So, be aware for your planning. IMHO, the visitors center is worthwhile and important to experience.

In taking everyone's sage advice, I think I will do a bus tour. Then head up to inverness, then Orkney.

Quick question - is there anyway I can fit anything around Aberdeen in there? The Dunnotar Castle looks amazing as well.

Yes, you can do train GLA or EDI to Aberdeen, and change there for Inverness.

The train goes through Montrose and Stonehaven, either of which could do for an overnight. A case could easily be made for 2 nights in Aberdeen giving time to explore the city or time to go up to Peterhead and Fraserburgh (or even Braemar and Ballater)- easy day trips from Aberdeen and both easy ones by bus.

I say about Montrose and Stonehaven because the 107 bus (see timetable- Dunottar is a stop, but isn't shown as a timing point, so trust me on that) runs between the two towns-https://tiscon-maps-stagecoachbus.s3.amazonaws.com/Timetables/North%20Scotland/Bluebird/Stonehaven%20Guide.pdf. (and scroll down)

Some on line sources will tell you X7 Dundee to Aberdeen- a previous fast bus. That sadly no longer runs Stonehaven to Dundee.

Afterwards the c 2 mile walk back along the cliffs to Stonehaven is just breathtaking. From the Castle you will see a big circular temple looking structure on the cliffs. You go past that, which is the Stonehaven war memorial.
No one regrets going to Dunottar.

Resources for Orkney (there used to be a proper integrated timetable for air/bus/ferry but that seems to have not yet restarted post Covid)-
1. All of Mainland bus timetable-
https://tiscon-maps-stagecoachbus.s3.amazonaws.com/Timetables/North%20Scotland/Highlands/Orkney%20Guide%20from%20Sunday%201st%20%20October.pdf

Best value day ticket is an Orkney Day Rider at £7.70

On Eday and Westray the bus is dial-a-ride in the winter.

1. The Inter Island ferry system-
   http://orkneyferries.co.uk/timetables.php

2. The Loganair page about inter island flights. As you'll see sightseeing flights are booked on the day and are £45. Don't be fussed about timetables ending late Feb. They are changed every few months due to daylight hours at the airstrips, but will be running broadly to these timetables if anything with the odd extra flight or slightly later timings. With the time the greatest fun for an islandophile like me is ferry one way to each out isle, air the other way. It's real old style simple aviation, in the very best way possible. I don't know any other airline where you can still get a printed timetable for starters.
   https://www.loganair.co.uk/fares/orkney-inter-island/

3. If you wanted to visit Rousay (as has been suggested elsewhere) it is a big island, and the local bus has stopped. So you would need a tour- https://www.rousaytours.co.uk/tour-information

4. If you wanted to go over to the big Island of Hoy (well worth it, but maybe not the best use of your time)- see the Community Bus page- https://hoyorkney.com/travel/community-bus/

(it's included here as a general resource rather than you specific, and yes most people do it by car, but this is adding the other dimension. The bus service is such that although a public bus it is run more like a tour, you are an individual, not just a fare payer).