I have gone the other way and added a factory CD changer to my glovebox. I believe you will need to remove the glovebox door and then the the glovebox interior. All screwed in so it is easy. You will have access to the CD changer and it is just four small screws and unplugging the cable. You can just tie the end of the cable up, removing it would cause more issues than it solves. BTW, for the early models even if the car did not come with the CD changer the cable is there in the car. That made it easy to add the CD changer to mine.
You may want to search junkyards for a glovebox liner that does not have the cutout for the CD changer. Lots more space will be available in the glovebox then.