Secondary guns and torpedoes for an American Super Tiger

What dual-purpose secondary battery and deck torpedoes would suit the hypothetical American Super Tiger?

Retain the contemporary 5-inch/51 and avoid exposed torpedoes; the requested dual-purpose role is not resolved.

Exposed deck torpedoes are strongly rejected for a battlecruiser expected to fight artillery duels. The preferred secondary battery for the hypothetical American ship ordered in 1913 is the 5-inch/51. Its identity and contemporary availability are checked during the exchange. How it would meet the requested anti-aircraft role remains unresolved.