Hi Christopher,
When you press the upgrade button it initiates a
command which takes care of
everything including the update script. So really there's nothing to do or
that can be done unfortunately.
You could install your old MediaWiki version
(
http://download.wikimedia.org/mediawiki/) locally, for example using XAMPP
(
http://www.apachefriends.org/en/xampp.html ).
Then use your saved database, upgrade locally to the current version of MediaWiki, do a
database backup of that version (for example with MySQLDumper,
http://www.mysqldumper.net)
and migrate it to your production site.
hth
Frank