Take a piece of your heat shrinkable wire wrap (about an inch), and feed the laced cable through until the wire wrap reaches the plug.
Heat this with a lighter until it shrinks tight around the lace. (Be careful not to burn the plug, the lace or yourself!)
If you want, now is a good time to add a little bit of gold metallic paint to the base of the plug where it might show.
Feed the cable through your “F” type video adaptor until it reaches the base of the plug. (If you have trouble feeding the laced wire through the adaptor, you can put a small piece of shrink wrap tubing on the tip).