Upon reading the article I linked to more carefully, I see that you don't have to delete the old back up. You would just need to restore the phone as new.
In your case, since it sounds as if you're trying to get information from your old phone to a new one, you're not going to be able to use a back up from the phone with the encrypted back. You may be able to restore the new phone from an iCloud back up of the old phone. You should also copy photos from the old phone to your computer, make sure that your contacts are synced to iCloud (or whatever service you use).