How can I hide cords that run down the wall near the mantle?

Use a piece of garland drop down the side from your mantel to help hide/disguise the cord.

hide tv cords:

http://www.grandmashousediy.com/mantel-floating-shelf/

https://knockoffdecor.com/how-to-hide-tv-wires/

Wire mold is what is used in our log cabin.

https://www.legrand.us/wiremold.aspx

Add some green plastic garland to cover the cords. The garland can go across the mantle too.

If a permanent problem, you can buy channels that hide cord. If it is due to holiday decor, I would make it part of the decor by winding greenery, a garland or something like that around them.

place a tall real or fake plant in front of it. :)

Or cord covers - sold everywhere. Many can be painted to match wall color. Easy and quick!

You can purchase cord covers and then paint to match the wall.

Your local home improvement store will have raceways or plastic products that hide wires....I'm drawing a blank on the name but that type of thing should cover over them.

I use Wiremold in a townhouse that had concrete walls, ceilings, and walls. All it had were outlets in walls and nothing else. Owner wanted ceiling fans, dining room chandelier, kitchen ceiling lights, upstairs bedroom ceiling fan/lights.

https://www.homedepot.com/b/Electrical/Legrand-Wiremoldng f/N-5yc1vZarcdZgn8

https://www.youtube.com/watch?v=9JEy4vE9HKM

https://www.youtube.com/watch?v=A1HPW_pWPRU

Another option is to use a clear extension cord.

Make or use a fake candle tall enough to hide the wires and be part of the decor.