I found you need to tell them what to do, not what not to do, and need to explain in a very calm voice why they mustn't do something, without raising your voice. Also, agree with him as much as possible. It can sound a bit precious if other people overhear it but it works. (Also had one whose cry shatters nerves, so I completely get your need not to hear it.) E.g. if he doesn't want to hold your hand while crossing a busy road, just take his hand and say, 'I know we don't want to hold hands right now but it;s only until we are safely across the road. I need to know you are safe. That's the rules! When we get to the other side we can let go.'
Also, if a tantrum started to brew, I never used punishment, but self-soothing which is a way better system. If we feel tired and emotional, we don't feel better if people scream at us or shun us. We feel better if people give us space in a kind manner. I had a cosy chair with cuddly toys and blankets on it. If DC started screaming or being naughty I'd just say, 'You are upset and you need to let yourself calm down. Go and snuggle in the chair and as soon as you feel better come and tell me.'
If I needed them to apologise for something e.g. making a mess on purpose or being mean to each other, I would do the same and say, 'WQhen you feel ready to apologise, come back and tell me.' Sometimes DS1 would be sent back to the chair several times, but never as punishment. I;d just say in quite a sympathetic voice: 'Ah, you don't seem ready to apologise so go and snuggle again. Maybe read a book or cuddle your teddy until you feel ready.'
I know a LOT of people think this is snowflake breeding, but actually, DC had ver few tantrums as toddlers - maybe two or three each over the course of their toddler years. And they were utterly chilled but polite and appreciative teens too. Their friends always commented on how well we got on without any petty rows. I think it was due to this approach. Read the 'Positive Discipline' series by Jane Nelsen. There's one for preschoolers, one for children, one for teens.