I added this functionality to my boards (v6.3), and it's quite a bit more involved than you think. You've really gotta have a pretty good grasp of how things work imo.
editpost.php requires a fair amount of changes, mostly with inserting new code chunks (including a new query), and modifypost.php also requires a couple changes too (including updating a query).
The thing to keep in mind, is that you also want to have the pull-down menu select the originally entered value by default, and not merely default to the same for all of them which may inadvertently change people's selection when they are only correcting a typo or something.
I would recommend that you hire someone to do this mod for you if you don't know how basically.