The last battleships in a world without World War II

If the world wars did not interrupt battleship construction, what would the final classes look like and when would they be laid down?

Construction might continue into the 1960s with larger guns and automation, followed by a slow transition in which missile-and-aviation battlecruisers could outlast traditional battleships.

Experiments with 18-inch weapons, automated main and secondary batteries, and reduced crews would probably precede the missile age. A faster battlecruiser carrying heavy guns forward and missiles and aircraft amidships might survive as a hybrid after the conventional battle line disappears.