The first thing to address is that the average bomb of today is ten times stronger than the payloads dropped during the Crossroads tests and they wouldn't need as direct a hit then as they would now. For reference the bombs dropped - being similar in size as the bombs dropped on Hiroshima and Nagasaki - were about 25 kilotons. The Russian Strategic Missile Force deploys nuclear ICBMs with a payload capacity as high as 250 kilotons (multiple by 4 to 10 to accomodate for the individual 250 kiloton warheads the [url=https://en.wikipedia.org/wiki/RS-24_Yars]RS-24 Yars[/url] can fire in one missile) or [url=https://en.wikipedia.org/wiki/RT-2PM2_Topol-M]800 kilotons[/url] and the Russian military is committed to expanding their arsenal with the START treaties on the way out; they've already released a report indicating they're looking at nuclear torpedoes for targets like San Francisco or Pearl Harbor. So both ships would still be severely damage.

Even if they did survive too they would require parts no longer in production and likely no one has specs for and demanding means that probably wouldn't ever exist. It's not just taking sheet metal and riveting it to the hull to make them sea-worthy.

And let's not forget how [url=https://upload.wikimedia.org/wikipedia/commons/0/0b/Iowa_16_inch_Gun-EN.svg]fucking complicated Battleship turrets are[/url]. No one in this world is going to be capable of replicating that.

Ships like the Missouri too were far too expensive to refit for the modern era, even for the US military during the 1980's. You're also not likely to find the powder bags required to fire them, or make them anymore; they're not simple gunpowder that could be made out of piss and charcoal. The required cordite is probably a process that disappeared from the large-scale manufacturing process needed to use those guns.

Really, the situation seems like a absurd measure for a command structure that had long phased out the Battleship for reasons that'd be all too apparent for them when they get back.