I'm not sure that even the US Navy could force those straits without nukes. The British in WWI sure couldn't.
You are right about the U.S. Navy. The majority of warships in the Russian Black Sea Fleet have been in service for over 30 years and would not be fit for sea missions. Some were built in 1966. The Turks are afraid they will move to The Syrian Port of Tartus, so back to Check mate.