I wouldn't go that far, but I think that the real answer to your question is that there is no "by the book" method for which hand should be used to chop or count. You are simply required to chop and count. I chop away from the "thrower-in" (I hate that phrase, personally) and count toward the table.

But these are preferences and there is no NFHS mandated procedure, as far as I know.

Am I Using The Correct Hand? Let Me Think.
 

Thank God !!!

No specific mechanics for which hand to use on a throw-in. Use what feels comfortable to you (with the caveat of make sure you don't hit a player).

Now, what you may hear at many camps (although I don't believe it's an actual mechanic) is on an OOB call to stop the clock with the arm in the direction to which you'll be pointing. IOW, if you're T and, facing the court, the backcourt is on your left, a ball OOB off of the offensive team - you'd raise your left hand, then point to the left.

Jammed Fingers
 

Or hit the wall, jamming my fingers, like I did last week. And by the way, I have hit players, several times in twenty-seven years, usually after a held ball call, after I look at the arrow at the table, and maybe my partner. In those few milliseconds, I lose track of players around me. So far, no serious injuries. Thank God.