Moderators should be able to edit these comments, just as they can edit comments. While history (for both of these!) right there in the UI would be better, for comments it's been declared good enough that the history is in the database (so SE can investigate complaints against mods doing this). If it's good enough for comments, which are more visible, then that approach seems good enough for edit notes too -- let mods edit freely and log it in the DB.
This ability should be restricted to moderators until (a) there is more-visible history (UI impact) and (b) broader need is shown. Let's make sure objectionable edit comments can be edited, but this should be rare enough that flagging and waiting for a moderator should suffice.