I am quoting jdcavo, our Coast Guard expert here
You need an STCW endorsement for any non-domestic voyage beyond the boundary line, including a voyage that only transits the waters of another country. Link to the post
A sailing from Los Angeles to Honolulu, for example, is a domestic voyage even though it traverses the ocean and logic would have you thinking you need international certs. Seeing as NY to Texas is a domestic voyage, I’d assume you wouldn’t need the STCW II/2, as long as as jdcavo says, you don’t transit the water of another country.
Always good to be more qualified than you need to be, however.