The very premise of stealing a Soviet submarine wreck off the ocean floor with nobody noticing is pants-on-head insane. The USN thought the CIA was being moronic to even consider this plan. The USN's idea was a lot saner; to simply use submersibles to extract intelligence-relevant materials from the wreck underwater, not lift and take the entire wreck. No surface ships needed, much less an expensive purpose-built attention-drawing surface ship.