The easiest way is to talk to your system admin very nicely.
The whole point of Endpoint security is precisely to stop you copying anything onto removable media that can be lost or accessed on a non-authorised system.
If you copy files off onto the external harddrive without it being encrypted you could take those files and copy them off onto any other PC you felt like, or give them to a competitor.
It'll come down to, is there a business need for you to backup these files to an external device, if yes, then the admin will generally just let you do it, if no, then you're screwed :-(
When it comes to security, theres a reason why we don't let users exercise their own common sense and discretion.... We find, that on average, they have none.