The OP is an argument from the negative. Just because there are no specific references to instruments, doesn't mean God forbids it. Musical instruments in NT times were probably scarce, as people met in homes to worship. Maybe finding a lute player was tough.
King David was a king, and had access to the best musicians in the Kingdom of Israel. So he used them, and the singers to worship God. In fact, there is a consistent pattern of using music to come before God in the Old Testament, to prepare the hearts of the worshipers.
Really, the Bible says very little on the worship practices of either the Hebrew or Gentile believers. The great thing about singing, is that you can do it anywhere! Of course, I also take my flute into the woods on retreats and praise God in his creation, besides playing in church.
Such negative legalism. Yet God has not yet struck me down for playing flute in church. Strange how that works? Or does the CoC cult believe you lose your salvation for listening to/playing instruments in church? It's gonna be a big surprise for them on Judgment Day, when the trumpet sounds!
"in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed." 1 Cor. 15:52
"And he will send out his angels with a loud trumpet call, and they will gather his elect from the four winds, from one end of heaven to the other." Matt 24:31
I guess it is just lucky those angels get to practice for the Second Coming of Jesus. Will your CoC members be able to hear it, or will they just walk away because a trumpet is an instrument?