A 9.2-inch Royal Navy super cruiser

Would a Royal Navy super cruiser with 9.2-inch guns be badly disadvantaged against 12-inch-gunned designs?

Not necessarily, because it would seldom fight those designs directly and could be highly useful as fast support against cruisers and capital-ship upper works.

Likely opponents and missions matter more than a simple comparison with 12-inch guns. Alaska belonged to an allied navy, while the projected Japanese B-65s and British ships would probably have different commitments. A 9.2-inch cruiser is judged highly dangerous to the Deutschland class and useful as fast support for heavier ships. At Denmark Strait, such cruisers could approach from another direction and bring additional fire onto Bismarck and Prinz Eugen. Armor-piercing shells are expected to threaten protection at those engagement ranges, while high explosive could devastate upper works before a torpedo attack. That is an argument for aggressive supporting employment, with the destruction of the German ships remaining a counterfactual judgment.