If it were me, I would keep the capture under wraps, just so as I can sweat the fucker for a few days and make the US government wonder what the hell happened to him.
However, I find the story of this guy being there somewhat dubious.
If anything, they would have transported him out of the theater of operations immediately once hostilities broke out IMHO.
And with someone that sensitive the USA would have pulled out one of those stealth Chinooks.
And that leaves aside the fact that US generals are high-ranking bureaucratic animals that would never risk themselves out in the field like that.
Anyway, here is some confirmation for my theory about Azov being turned into informal commissars for the regular Ukrainian Army.