I think you're getting a really hard time here, OP. I have a four year old (four in September so older than most for her preschool year) and she still can't wipe herself properly after a poo. I have tried and tried to help her get the hang of it. We practise all the time, I make her do it first and then help her do the last bits with my hand over hers so she can feel where to wipe, I reward her for a good effort with lots of praise for really trying and what's more she really does want to be able to do it. But she hates the idea of getting poo on her hands, and it's nothing I've said as I always point out that it doesn't matter as long as she washes her hands and she always washes her hands afterwards of her own volition anyway. She's just a bit cack-handed (haha!) and generally clumsy.
FWIW, she is NT, reasonably bright (can read quite a lot, dress self adequately, count, add up, put her shoes on, hang up her coat on her named peg, write own name alone and other words with help etc etc) - she just hates the whole idea of getting poo on her hands, which strikes me as a perfectly reasonable position at her age.
Also, she is in a state-run preschool (stand alone, not part of a primary school) and she gets the help she needs at school when she wants to do a poo (pretty rare as fortunately her poos tend to happen just before bedtime, once a day every day). If they are allowed to do it at this preschool, I cannot think why they are not allowed to do so for your son. The help she gets ranges from actual wiping to someone giving her a wet wipe or two and showing her where to wipe but she has not been left to deal with this alone and there is no suggestion that she should be from the preschool. I asked them for advice about bottom wiping, btw, as they are absolutely brilliant, and they did say that these few months in a child's development between now and school can be huge in terms of the leaps that are made. Just because your son can't do it now, it doesn't mean he might not learn it in a few months, with plenty of help to do so.