From the hints that the article gives, I believe the cruiser involved as part of the deal may have been the unfinished Slava-class Admiral Flota Lobov (later renamed post-Soviet collapse as the Ukrayina).
Given the description of the submarines as "old and diesel electric", the Soviet tendency to keep warships as long as they could float, and how complete Ukrayina got, it is highly unlikely to have been that vessel.
News reports from the time (May 1989) are clear that the vessels were being sold as scrap so my guess is the cruiser, assuming the news reports were accurate, was a Sverdlov. Several were scrapped in the earl 1990s and I would suggest any one of them is a potential candidate for the Pepsi cruiser. The frigate and destroyer would likely have been of similar vintage so a Riga class for the frigate and at a push a Kildin or a Kanin for the destroyer are strong candidates.
You're probably right. I misread part of the article to mean that some incomplete warship construction was part of the scrap. More than likely it was actually referring to the new build tankers element of the deal.