It's best to still "keep" the cache folder, because it's not only sql query-caching that uses that folder. The PHP session system also stores its cache there. Thus, deleting the folder entirely is not advisable.

Simply moving it by drag-and-drop with your FTP software, and then updating the 2 configure.php files and the Sessions Directory via the admin ... should be sufficient.
Alternatively, deleting the old one, creating a new one, and making the new one read-write ... is effectively the same as drag-and-drop in FTP.