This is my challenge: I have a 60" 4K UHD TV, Home Theatre System, 4k Blu-ray player, and cable box. The guy who installed them ran all cables through the wall. I need to switch one of the HDMI cables because it is not 4K compatible. Unfortunately, it goes from the surround system (output) through a hole in the wall, to another hole to the TV (input). I tried to tape them together. But as I pull the cable, it does not move easily, as if it were fastened down.
It is likely that the cause of the friction on the cable is from the cable making the turn through the box's. Many time the boxes that are use to retrofit the hidden wiring for TV's are OLD WORK BOX'S and can be removed to run new cables.
Push the cables a little into the the wall through the box so there is slack cable in the wall cavity. Then you would loosen the screws that tighten the wings of the box and and gently pull the box out of the wall, you may have to push in on the box as you turn the screw to get the wing to free up from the back of the wall. Because you pushed cable slack into the wall you Now have the box's hanging out of the holes in the wall but the wires are still running through them.
Now work the ends of the HDMI cable backwards through the opening in the box just so its end is out of the back of the box, you want both ends to be free of there box's.This frees it up so it is not binding on the box and is loose in the wall ready to be pulled. You may not need a fish tape or to tape on the new one if you can just feed the new one into the wall from the top and until you see the end through the bottom hole, unless there is horizontal blocking in the cavity that has been drilled for the wires, this will requite a fish tape to pull it through the blocking . If there is blocking i would tape a fish tape onto the old wire and pull it up through the blocking so you will then have the fish tape in place to pull the new wire back through.
Once the new cable is is run through the wall and both openings you would then push the ends of the new HDMI cable through the back of the box openings and pull enough out to reach the tv and the other device and reinstall the box's.
This YouTube video show an installation that may have a similar set up as yours or not but it is helpful to show the old work box mechanics and fishing wires.