This page here
http://ez.no/doc/ez_publish/upgrading/the_system_upgrade_scripts givs you an overview what each script is doing and when they are needed. If you update from 3.8.3 to 3.8.4 you should not need any script at all as the correctxmltextclasses.php is necessary for updating to 3.8.1. So the changes should already be included in 3.8.3.
With regards to the cache: As far as I know you can delete everything in the folders /var/cache and var/<site_access>/cache. To be on the safe side you should of course make an backup but I usually delete these folders manually if I move an installation from one server to another and had no problems yet.