Perhaps the real issue here is not about hitting or not hitting, but that you cannot be mechanech your children with faith, compassion and integrity if you are fundamentally lacking there.
And, through no fault of your own, you obviously are.
A person with emunah does not feel so threatened by a sleepy 9 year old bookworm, or so fearful of the possibility of him not going to minyan when he’s 14, to be compelled to be violent with him. So harsh with such a young child. One would think he’s skinning animals alive, the way you speak of him.
A person with emunah does not “need” his child to keep shabbos. He “needs” to do his best in his own avodas Hashem (including chinuch) and then trust that Hashem has given each person the privilege of being responsible for his own life. If you had a meaningful connection with Hashem and His torah, you would care most that your child has that real connection too, and would not prioritize hollow practice of rituals over the pinimius of them.
An honest person does not create a false dichotomy between a) continuing with a few halfhearted, failed parenting strategies (making charts, taking away books) and b) hitting. He would see that there are, in fact, an infinite array of creative options, and plenty of wise guidance, available to him.
But first and foremost, a maamin would do some deep prayer and self examination. Hashem has obviously given you this child to bring about YOUR growth, and probably healing from your own childhood. You distract yourself by demanding change in that child, but the truth is, you do not believe that you are capable of change yourself. As long as that is the case, you will fail to inspire change in anyone else. (Similarly, you likely feel self-loathing for your own struggles with self-discipline and that’s why this child’s behavior enrages you. כל הפוסל במומו פוסל)
You are not being honest with yourself or with others. You say you are worried about your child not going to minyan in 5 years, but really you are just angry about missing your train and having your will generally frustrated by this child. There’s nothing wrong with that, it’s very normal, but for some reason you can’t own that this is about your anger and shame. You assert that you are discussing a hypothetical child, when in fact there is a very real 9 year old in your life who makes you feel helpless. You distract others with philosophical discussions of corporal punishment. Because if you were honest about what’s really happening, you might have to take steps toward actual change, and that makes you feel more helpless than anything else.
It’s not your fault. You were likely raised with the same attitudes that you show here and are unwittingly instilling in your own children now.
You know, a helpless person can always cry out to Hashem sincerely, over and over again, until something shifts — maybe just an insight. If only you really believed in Him, and His rachamim! Instead here you are picking fights in the coffee room, seeking permission to smack your child.
Instead of waiting until this child is 14 to run to experts for help, why not go to those experts now? If you are willing to confront yourself, an expert may help you sort through some of your very damaging beliefs about yourself and others. Either way, I hope one day you see that love and connection is not the weak choice for you, but actually the harder, more courageous choice.