Would larger County cruisers require a Japanese battlecruiser response?

Would 9.2-inch County-class cruisers require Japan to send a Kongo rather than its cruisers?

Probably not, because Japanese cruisers would likely carry 9.2-inch or 10-inch guns in the same scenario.

Japanese cruisers are expected to carry 9.2-inch or 10-inch guns if British County cruisers receive 9.2-inch weapons. Japan would therefore still be able to send cruisers, as it did historically. A fully developed County design might outperform Exeter, but the hypothetical does not make a Kongo necessary.