Yeah, Doomsday tends to get a pass from even the staunchest 'never kills' advocates. As has been said, the degree to which Doomsday is even fully sentient is up for debate and in most regards the thing was little more than a rabid animal. It was also perhaps the craziest slugfest post-Crisis Clark had seen and maybe the tightest corner he had been pushed into, the threat to innocents was very direct and real.....and in the end Doomsday didn't even stay dead. Real easy to justify this fight.
Whether Clark thought Henshaw would survive is much more open to interpretation, and I think perhaps it's Clark's intent that really matters here. He knew Henshaw was a technopath and so might have survived being shattered. But Henshaw was also beat to crap and had a fist put through his chest, it'd be fair to assume the man might struggle mustering the concentration needed to escape. He 'could' have died there, but what did Clark 'hope' would happen? Did he break Henshaw hoping the man would die, or with the presumption that he'd live? I read the scene as Clark going for the kill. I don't remember any attempt to contain or imprison Henshaw and Clark didn't have the resources to do that anyway, so destroying the body just forces Henshaw to become a ghost in the machine; harder to find and arguably more dangerous. I just don't see Clark letting that slide. One thing for the villain to escape despite Clark's best efforts, another thing to help that along. No, I think Clark was going for the kill, hoping it'd stick. Just like when he shoved Henshaw into the Source Wall a few years later: a genuine attempt to put an end to something that's functionally immortal.