Popping off the door panel is actually pretty easy--it's just a bunch of plastic clips around the edge. If you're brave, you can do it with your bare hands, or you can use a screwdriver to pry the panel at each plastic clip. Make sure you remove any screws that might hold the panel to the door frame--they can be in the grip that you use to close the door, the handle for opening the door (which you've already removed), and also behind the speaker grill closer to the floor.
Once you've removed the panel, it should be easy to access the cable to replace it. Alternatively, if you're feeling slightly adventurous, take out the whole cable, insert the cable strands into the sleeve, and whack the sleeve a few times with a hammer to crimp the wire inside it. Then put the whole thing back together, and hope you don't have any extra parts :)