I think Italy and Britain lost a total of 90 destroyers this afternoon in various naval battles (not counting the CAs, CLs, and a list of other ships I can't remember).
Many of the hits and kills came from non-NAV sources.
Of course, if a carrier has planes that sink another ship, I still consider that a ship on ship kill.
I sank the entire Turkish navy today with the Black Sea fleet in a contest that included WWI era Soviet battleships slugging it out with a WWI era BC that Turkey had. No significant contribution from air power from either side. (Submarines helped finish the Turks off this time.)
Sure, pursuing enemy ships into air cover protecting them can be dangerous, but depending on the Allies approach, the Axis may not have coverage over every port they might retreat to. Especially earlier in the war, it's a big globe with lots of air regions to fill. And naval air regions can be quite large outside of the English Channel and the North Sea, limiting the effective number of aircraft that can even be employed.