It's worth noting that there are non-cognitivist positions other than emotivism (the "boo, murder!" position). For instance, there's the prescriptivist position — that moral claims are imperative sentences or commands. This is also non-cognitivist, because commands are not propositions and don't have truth-values. But it's not emotivist, since we can do a kind of logic on commands, even though it's not the same as the logic on propositions.

https://en.wikipedia.org/wiki/Non-cognitivism
https://en.wikipedia.org/wiki/Imperative_logic

("Boo, murder!" does not logically entail "Boo, murdering John!" ... but the command "Don't murder people!" conjoined with the proposition "John is a person." does seem to logically entail the command "Don't murder John!" So conjunction of commands and propositions works. But disjunction on commands doesn't work.)