That's one good thing about the recent change in the NCAA team control rule. Since there is now team control during a throw-in, you don't have to use the arrow.
For NFHS, if you really want to get it right, you have to use the arrow, and if it is going the other way, you'll get to throw the coach out.
A funny solution which you could use, and still do it by the book, would be to administer the AP throw-in to the opponents and as soon as the kid passes the ball, blow your whistle. Now you have another accidental whistle and the arrow is going back to the team which had it in the first place.
If the first arrow allowed the original team to retain possession, then simply have an accidental whistle during the next AP throw-in and fix it that way.