Returning, I don't think Gills Bay or Thurso will have a one-way car rental.
Hertz have an office in Wick between the town centre and the airport, so one way car rental is certainly possible and it is very easy to get there by public transport from either port.
Personally, on Orkney, I prefer to stay in Stromness as opposed to Kirkwall. I find it a more interesting town, especially in terms of the work of the Hudson's Bay Company (relevant both to Canadians and those from the PNW), the town's layout very much being a legacy of that maritime history.
Granted some of that history sits uneasily with us nowadays, looking through modern eyes.
Stromness is as easy for public transport as Kirkwall is, and makes little or no difference if by car. The only difference being that both car rental agencies which used to exist in Stromness I believe have closed. Landing at Kirkwall from Aberdeen at 11pm you may not want to drive 30 minutes across Orkney Mainland- although the X10 bus from Hatston to Stromness also does the journey every night.
The place I always stayed at in Stromness (a lovely old building converted into a B and B) did not survive Covid.
I actually have the same issue in Kirkwall, in that almost anywhere I used there has closed- including a wonderful apartment just close to the inter island ferry dock. It had a huge level of repeat business so was very hard to get into. For a week in December using entirely public transport to reach parts of Orkney and the out isles never mentioned on this forum it was a great cozy hideaway. Looking on Google maps for Kirkwall itself Eastbank House is the only still open place I've used- and I am not 100% convinced that they are really still open- whatever Google maps says.
One trick of the trade is to use the B and B offer on the MV Hamnavoe the night before returning south. You board the previous evening at Stromness when she docks on the last sailing of the night from Scrabster, and sleep on board before her 6.30am departure next morning. I'm up early to see her slip her moorings, then get my breakfast as she rounds the Old Man of Hoy.