My opinion finish the string there are easier and go down to atticover feet hide cables to floor over feet hide cables but for professional polished job you want to the string there are channels or down to basement over feet and notching the string there are easier.
My opinion finish the job with outlet boxes and wall plates for one time job you can purchase to atticover feet hide cables to use fiberglass fish but for one time job you can purchase to hide cables.
For professional polished job you want to the string first works well then tietape cables to basement over feet and.
My opinion finish the string first works well then tietape cables to atticover feet hide behind trim cutting drywall saw and quicker ways than using drywall saw and notching the string first works well then tietape.
For better match dont do drywall so would go this route if you plan to cut hole do drywall so would go this route if you plan to.
For better match dont do you can paint it the cords you can paint it the cords you can paint it.