A very difficult subject,
YABU to think that smacking a child is the same as an adult.
A duty of care extends to a child in your care and at some point that duty might extend to what jerry said (a last resort or he will throw his sister under a train) which we maybe condone but understand (and the law justifies to a certain extent and calls it "lawful chastisement" in certain circumstances). That duty of care extends to not exposing them to harm, from themselves, from others and the environment.
You do not have that duty (in the main) towards adults nor can you "lawfully chastise them". However you can defend yourself from them (again the law can justify this "self defence" if your actions are "reasonable" in the circumstances) this would not be something you would be justified in using towards a child.
Elder. This is one incident of violence, you have admitted it on here (big step) and have resolved to do something about it. You have rationalised why you did it and come up with the answer that you were wrong. And I think it was wrong- you lost your temper. You are hurting far more than the child.
It is unlikely that you are an "domestic abuser" from what you have said. Ask yourself, do you indulge in a range of behaviours to control and dominate? Unlikely, from what you said.
There is a child, probably living in your town, who has never been smacked, yet has not got enough to eat, is left on his own whilst mum goes out, is never washed, is deprived of every human dignity, is cold, is told that he is scum and lives in a place (not a home) with no comfort, no food in the cupboards and no love.
I think that child would swap one smacked bottom when having a nappy changed that he might never remember, that never happened again, for years of neglect.
Good luck and love your son, he will forget the smack.