Following a suggestion from someone else on the Steam forum, I was able to find an almost 30 year old fix!
Dr. Who's Harpoon Pages
https://www.harpoonpages.com/harpoon1.htm
The 4/04/97 update can be downloaded and imported into the Harpoon Classic 97 folder to replace the NAVC.res file (I created a backup of the original file just in case). When I ran the scenarios using that updated file, the ships all appeared correclty as Okean class instead of Kalinin class.
The website also includes an update for the EC2000 scenarios. Were there any old bugs you can remember from those scenarios - anything I should look out for before deciding whether to apply that update as well?