Another option is to do a mysqldump of your entire database and import this into the new server, and copy over the whole courses directory. This would port all of your existing courses, and you could then delete the ones you don't need. This might be less work for your system administrator, but possibly more work for your WeBWorK administrator.
In my experience archiving courses in a previous version of WeBWorK and then unarchiving in a newer version often runs into problems, particularly if there have been database changes between the versions, but YMMV.