Current DD took erad's hv to the face to no effect and then impaled him like he wasn't there. He was able to not only hit the Olympian (even with divine grace) every single time--when people like WW could not--but also KO him. Current Henshaw blitzed this guy in half.
Then even with his regen taken away, fought DD until he was little more than strips of himself. My point being that even if this is an insta-win via destruction of the body or near destruction, it's going to take a lot for Henshaw to even begin to wear down. So near destruction-- in this battle-- becomes a relative term, unless by near destruction, what is being referred to is an instance like the galaxy buster in sc, the willhunters arc in gl, or even the DD instance.
With that said, in a comic book, Superman would simply find a way. The same as cupping "bleed" in his hands, singing the god of evil to death, saving the omniverse, or nearly killing someone that the avatar of death and the void couldn't see.
In a forum battle however, he loses to henshaw. Keep in mind, Henshaw is fighting at full capacity.