I'd think that King David would have purchased TOL instruments(he could afford them) and he as a skilled musician would have "played" them as Chas noted.   Also, judging from the records of him, he would not have been per-occupied with the tools themselves, but rather used the tools to express himself through skillfully played music.   After all, he was known for doing his worship music with all of his heart and passion.  As the saying goes, "It's the painter not the brush."

By the way, David didn't really have to think of Bathsheba as she ended up being his wife after David had sent her husband to a fierce battle where David knew he would certainly die. It was to cover up a murder.   David paid dearly for his action.  He was dealing with a "terrible" God, who one time killed 70,000 people just because David took a census though he was told not to. It was prophesied that what King David did in private, the same will be done to him in bright daylight.   It happened to him.  He lost his child he had with Bathsheba, his kingdom torn in half, and his own son violated his wives and concubines in broad daylight.