Depends on the Superman I suppose, each “era” is a different guy.
I think Post-Crisis Supes would be the one guy writing an article about how the world failed Walter Kovacs and that in spite of everything set against him, Rorschach made a difference and gave his life to expose a cabal of hypocrites, one of which was the only man he ever called “friend”
(Nite Owl in Snyder’s version is an improvement) and they all were tested and found wanting, except for the homeless incel who stank and associates sex with violence.
That’s the kind of guy I think Post-Crisis Supes is, he’d be the one guy writing about who was under the mask of Rorschach and the one man who cared about Walter Kovacs and would respect the sacrifice. So yes, I think Superman would shake hands with Rorschach because though broken by his world, Rorschach embodied Truth, Justice and the American Way.