Quote Richie Royale:
In Cubase you can set a new project folder and backup the arrangement which will then be the new target folder for audio files. I would expect that Audition can do this, but I would suggest referring to the manual. On Cubase it is in the File menu, so have a look there first.
So instead of just copying the folders to the external HD and deleting them on the internal HD, you can do a backup within Cubase that re-maps the DAW to the new folder and file locations and allows you to continue your editing of the old files and arrangements in the new folder on the new external HD?