I don't see any reason he couldn't lift it. I think the various stories showing he would kill are reason enough to say that he could lift the hammer if Death is the only thing stopping him. Lord Superman, Superboy Prime, The High Councilor, Ultraman, and Brutaal are all Superman willing to kill. Lord Superman and High Councilor are probably even more correct in their judgement (overall, but not case-by-case,) to choose to kill people like The Joker and Doomsday. I have to believe that, given the fact that it's infinitely possible that Superman would kill someone under the right circumstances like any of the other "warriors" discussed here, he should be able to lift the hammer.
And I guess when you put it like that really anyone could lift the hammer. I'm not huge into Marvel so maybe I'm missing something, but perhaps there are some universes where Thors' analogue is unable to lift the Hammer?
The problem is you are looking at Odin's idea of worthiness. Superman's no-kill philosophy varies from absolutely no to under extreme circumstances depending on the writer and version of Superman. At the end of the day, Superman is not a warrior which is what sets Thor and Superman apart. The killing aspect is a part Walter Simonson once stated to indicate that difference.
Superman should lift it because his soul is more pure and divine than Odin's andt hus should break his enchanment by sheer force of willpower. I mean Superman is God made more Holy than other Gods.
I know in DC Superman is often portrayed as some sort of universal messiah, but again you are comparing something closer to a Christian idea of worthiness to a Viking idea of worthiness. In many stories, Superman is vulnerable to magic and Mjolnir's worthiness clause is magic.