I guess something like missile cruisers but battleship sized might work? Or am I misunderstanding why cruisers survived while battleships didn't? Agree with FriendlyGhost.
Realistically the Battle ships still had use post WWII, the USN, RN, and French would all keep some around, some longer than others. The war had shown that they were vulnerable to aircraft, but that could be largely negated if battleships were escorted by their own aircraft from carriers or land. The real reason they went away is that there just wasnt any use for them after the second world war. The Soviet navy never built any battleships, once that became clear the western navies found the ones they had to be way to expensive to keep around with the exception of the USN which kept some just in case.
Cruisers and carriers on the other hand stuck around because they were still useful. The Soviets built alot of cruisers so keeping some of your own was a good idea until the missile age came along, and while the USSR would only build a handful of carriers late in the cold war a carrier was still a very useful tool. Capable of delivering lots of destruction very far away as well as providing recce and ASW capability.
In a scenario where the Soviet Union completes some battleships or battlecruisers the type probably sticks around for a bit longer. Though eventually the type will be rendered obsolete with the introduction of practical ship launched missiles early in the cold war. Maybe they last about a decade more with the USN retaining more than just the four Iowa's, maybe completing the final two or a Montana, Britain probably retains Vanguard and maybe a KGV or two longer while France keeps Jean Bart around as well.