Actually, though, with the right choke hold blood flow to the brain is also cut off. While Supergirl and Superman don't need to breathe, they still do need blood to the brain. So, while they wouldn't technically pass out from the lack of O2 to the brain they would eventually give in due to the lack of blood flowing…

As for Hank, he's giving me more of a "martian manhunter" vibe than "cyborg superman" that he's named after. Plus he's actions so far have been nothing but heroic in an odd sort of way.