[OP] I agree with your decision not to hit your kid. This is negative reinforcement and the end result is that he will inhibit specific behaviors only because he fears the punishment (an ass beating, a cold shower). You’re best saving the negative reinforcement for extreme situations. Wiping shit on the walls could be one of them. However it is a slippery slope. Once you and your wife feel contempt for your child love really is lost and it can become easy to take the negative emotions he is invoking in you out on him and then regular beatings start. I think it’s important that you look at the situation scientifically so that you do not feel contempt.
That said, what kind of advice could possibly help you? That’s a really difficult problem. Keep in mind that your son is still at a very sensitive age of neural development and the experiences he has in his life now shape who he will become. It’s important not to lose sight of the goal here: a normal, healthy brain.
It sounds to me like your son’s reward centers are not properly wired. He doesn’t have a clear understanding of the relationship between punishment and reward. “Understanding” means to me, literally, that the neurons in his brain simply haven’t had the life experiences - combined with whatever random genetic propensities he was born with, which is not his fault - that lead to healthy neural development. This is qualitatively different from a chemical imbalance, although it certainly involves chemicals. He needs to have positive learning experiences involving both reward and punishment so that his basal ganglia can start to approximate that of what society considers normal. Learning, learning, learning.
One of the best ways to teach is through repetition. It will be difficult and very effortful for you and your wife to get in enough repeated trials of positive experiences involving punishment and reward. Thus, I have the following highly nonstandard suggestion: Allow your son to become addicted to video games. Forget the nonsense you’ve heard about it leading to violence. It certainly doesn’t lead to shit on the walls. There are boundless positive experiences waiting for him in virtual worlds and his young brain will eat it up. If you have nothing else, it’s worth a shot IMO.