We've found it's better to delete the old set of folders and then copy in the new set. This is because sometimes a file was deleted in the new version, but doesn't get deleted when you copy a new version over top of an older version. As you said, you do need to retain your settings files. You will not need AdminSettings.php for the 1.15 versions if I read the release info correctly. You also need to retain the images (uploads) folders or anything uploaded to your wiki will be lost.
If you have a different folder (with all wiki code) for each of your 30 wikis then they definitely do not share code with each other (unless someone has done something overly complicated.
Yes, mysqldump like you wrote to make the database backups. It could get a little fuzzy if they share a database, but the settings should be able to handle it.
Good luck! -Courtney