Traffic lights and similar systems can work for children who have some control over what they are doing and are motivated by reward, but they are not so good for children who are basically responding in panic or overreacting because they have fallen out of their "window of tolerance". I have linked the Beacon House UK video which explains the about what is referred to as the window of tolerance, that when within it children feel good, at their personal best, calm, relaxed, able to play and learn, but when not in their window of tolerance - not calm - children may appear or be aggressive etc - and also how to help them back in and expand their window of tolerance over time by talking about feelings. It might be worth sending the head and the teacher the video or explaining to them what it says, and explaining that helping your dc calm down and reassurance is more likely to be productive in relation to behaviour - that might be getting down on his level and reassuring him, saying "we can be calm", or whatever strategy you have which works. If the teachers and the children see positive changes from helping your dc be calm rather than using punishment or consequences or traffic lights that will help with interactions at school. It will become easier to see where his triggers are too.
In relation to at home, pretending you don't care about the hitting or using consequences may in fact make worse because it makes your dc feel less connected and therefore more in fear which shows as anger. Staying connected and reassuring your dc with words and talking about his specific feelings as well as about feelings in general, and doing things which will help calm his nervous system, whether it be walking or banging a drum, might all help. The most important thing is that he feels you have his back and that you will help. Consciously spending time with him doing something he enjoys at the weekend, whether it be dinosaurs or animals, will help. When you do find him calm and happy make sure he knows the word to associate with the happy feeling - "you seem calm and happy"
Also teaching him about expectations ie "we don't hit" a lot so that that is firmly there in his consciousness as that will help over time, when he raises his hand to hit he will remember the rules and do his best to follow them, and teach him alternative ways of dealing with anger or fear using words, such as saying "I feel angry" or "please don't do that" - it is a question of repetition.
His self control is likely to be behind his peers (of 4 - 5 years) but by doing the above consistently he can catch up, consistently going in the right directon is more important than catching up speedily.
He may enjoy watching these videos, the first one shows children being friendly to each other and just watching it can trigger some positive things for him:
NB - be vigilant about children being unkind at school, this can happen in this year group, your dc may struggle to explain what is happening or recognise it, so by talking to him every day about what each of the children did during the day and what they said to him and who he likes can help you see patterns (you helping out in class can help here too) and it will also be helpful for both of you learning to share your thoughts and feelings and you guiding him when you see his thinking is going off track. A book aimed at his age about making friends might also be good to read together.
This is the beacon house video about the window of tolerance: