Yes, you can orphan your work at any time, it doesn't make a difference if it's part of an exchange or not.

To orphan, you hit the edit button for that fic, and at the top of the edit page there will be an 'Orphan Work' button. (It's between the 'Add Chapter' and 'Delete Work' buttons.) You'll be taken to another page which will ask you if you're really sure about orphaning, and whether you want to keep your pseud attached. You can cancel or go ahead, but remember once you orphan you can't undo it.