This is just a complete load of rubbish, this is just a little 4 year old child not a teenager.
OP my ds went through a delightful stage of loving slapstick when he was slightly older than your son, unfortunately as part of this he loved tripping other kids over and watching them go flying. Thought it was brilliant! Obviously I was mortified. I caught him 3 times over a period of a couple of years and I'm sure there would have been more times when i wasn't there. He couldn't think of the possible consequences of what he was doing or empathise with the kids he was doing it to.
He also knew he was very clever and had no problem boasting about it, he couldn't understand why other kids might not get things as quickly as he did. Doesn't he sound a delight? But still he's now a young adult working as a software engineer and studying for a degree, fitting in well and enjoying it all.
Pre-empting people wanting to speak to him is a great idea as suggested by pp, but you can't do that forever. I would alongside that discuss with him and encourage him in socially acceptable ways to get people to back off ie 'No thank you'. There's obviously loads of ways you can practice this at home yourselves and he can see how it can give him control over situations.
If situations arise where he could say it then just remind him like a stuck record like you would with a toddler - if he's rude and 'I think you mean no thank you ds' is going to be too anxiety provoking for him then perhaps 'oh that's a really good time that you could say 'no thankyou' ds and then I'd know you don't want to.' Of course if it catches on do not expect him to realise that 'no thankyou' won't get him out of things he really has to do! Also expect it to take time for him to get it and start to trust in it. See if he'll practice it with you with you asking silly questions like 'do you want seaweed for tea' - it's hard to know how receptive he is to learning social skills like this or if bringing in humour works with him.
To me everything you say fits with ASD, I'm not really sure why you think it doesn't? This is a kid that clearly has absolutely no idea about social rules, what's socially acceptable, his own emotions, others emotions, despite being a very bright child in other ways - it is all completely typical. He needs so much teaching of very, very simple basic social and emotional skills, the sort of thing that is completely obvious or even kind of innate in other kids. He won't have a clue, I was amazed at the things ds didn't realise that were so blindingly obvious to me that i didn't think anyone would need explaining.
Your ds needs every little thing explained to him when it comes to these things - he probably doesn't have a concept of 'sadness' or recognise when he's feeling happy. He can't understand what someone else is feeling when they are upset or angry, he won't even recognise those things. Explain to him what he is feeling as he is feeling it and why - oh I can see you're feeling really happy because x happened. Also try using his past experiences to help him understand others, 'remember when you fell over and hurt your knee and you were very upset, well now x has hurt her arm and is feeling like you did then.' He may still be a bit young to really get it, but it just starts the process of understanding and learning about emotions and empathy.
All this really needs a lot of time, effort and input though OP and that is going to be tough if you're also working full time. I don't suppose there's anyway you could reduce your hours or go part time? I was a SAHM when DS was little and tbh I think it made a huge difference to him feeling safe and secure, having a lot of 1 to 1 time, a lot of opportunity to just decompress and not have to be around other people constantly and for me to work with him the skills that he struggled with. How does he manage at school/nursery? Is he masking there and seems absolutely fine? Please don't think that will prevent him getting a diagnosis if so, ds was perfect at school.