Code editor with key authentication
You haven't really asked a direct question here; But I assume you're asking for a code editor which supports SFTP key auth?

In which case, Coda 2 has built in support for each type of connection (including key authentication).

If you're after a free alternative, I'd use Cyberduck and Sublime Text. If you open a file from Cyberduck (into Sublime Text), it automatically uploads each time you save.

If on the other hand you're looking for a way to use key authentication within Dreamweaver and the software simply doesn't support it, there's no way solve that.