I've replaced brake cables w/o removing the housing. You shouldn't need to use needle-nose pliers to remove the cable...just pushing the cable from the brake side where it enters the housing will push the plug-end out the front of the brake handle.

No need to loosen the barrel adjuster as once you release the fixing bolt, the cable will be loose.

For installation, angle of attack is critical...don't force it...use a flashlight. If you're unable to solder/file the end, I find slowly turning the cable in the opposite direction of the twist (so I think that would be counter-clockwise) helps the cable not to unravel.

Use a rubber band to band the brake handle to the bars to hold it open so you have both hands free (flashlight in your mouth, of course).