"If I make sure he does can (blank) have a shower tomorrow morning. Also how do you say hi in sign language"
It's readable but difficult. For teachers that see him regularly, like his primary ones did or in more frequent secondary subjects like English/Maths, the teacher would likely be able to decipher it due to familiarity.
Unfortunately, it will be more difficult for someone with less or no contact to be able to read what he is trying to communicate. For examiners, whilst they will try, some PPs are right when they say that there isn't time (or in some cases, the ability) to fully decipher everything and so the marking of his exams may not always be accurate. I'd be expecting him to make use of transcription at least (adult reviewing whether something is legible at the end of the exam and asking him to read out anything that isn't so that he/she can record it alongside his response).
The question is whether this difficulty stems from a physical or mental source (or both). If it's physical then there are things that could help (pen grips, writing slants, etc.) Benefits could be instant but the overall impact may be low. If mental, there's the possibility that neater handwriting could be trained through repeated practise and effective regular feedback. However, this would be a long process as you're essentially "rewiring" the way you write.
We have children who use a range of assistive technology from simply typing instead of writing to those who use speech to text systems to dictate their work. It really isn't as rare as people may think. If you think he needs this, speak to school and so if they can help address his fears around standing out negatively.