Could Second World War battleship shells be guided?

How would the war change if 16-inch shells had GPS guidance?

GPS requires much later infrastructure; radio guidance is more conceivable, but making the control system survive firing would be extremely difficult.

The answer separates navigation infrastructure from projectile engineering. GPS guidance first requires a satellite system that lay decades beyond Second World War capability. Radio guidance is more imaginable, but the shell still needs control surfaces and electronics that survive firing from a 16-inch gun. The extreme acceleration and shock make a plausible guidance concept very different from a practical battleship projectile.