What about adding a "Disagree" button? And show the text "Some disagree with this", if some people disagree. Or "Many disagree", if many disagree. — So, there'd be two kind of downvotes. One for "disagree", and another for "I don't want this kind of comment here at HN" (currently HN in practice only has the last one).

Look, a demo of how this can work and look: https://insightful.demo.ed.community/-7#post-3

— scroll up just a little bit to see the "Some disagree with this" warning just above the comment. And if, below the comment, you click the `V` button, to show various types of votes (in addition to the Like vote), you'll see there's a Disagree vote.