Is the lappy to ease the amount of handwriting? I can fully understand him not wanting to appear anything other than one of the lads at school, at his age it's excruciating for him to be seen as different in any way by his peers.
If so, ask school to provide notes of each lesson rather than him writing them himself, they did that for my dd as it was outlined in an assessment, think it was sometimes another pupil's notes photocopied. (Don't know if that's acceptable these days but do ask)
In fact, the notes could be scanned and emailed to him, rather than given to him in front of the class.
Also in his assessments, he should have exec. function, processing speed, handwriting speed etc.tested so depending on the results of that, he MAY be eligible for a reader and/or a scribe during exams. You can look up the criteria on the exam board's pages, it has to be applied for ages in advance.
Can you let whoever is doing the assessments know that he's terribly self-conscious about being seen to be different in any way so can they suggest any ways to help him that the other kids won't pick up on. They must have experience of this.
Can you email SENCO and say the same, ask how they do things to avoid pupils who need extra help being singled out and open to taunts etc. They must have experience.
He probably thinks the assessments are to find 'something wrong' with him, do explain that's not the case, they are to find his strengths alongside his weaknesses to help him at school, in FE or Uni and in the workplace.
Really really, really stress that being different is just that, different is NOT inferior, different is NOT odd, different is NOT wrong, just different.
Young kids like the comparison to computers, Windows is used by a lot of computers, Mac is used by a smaller amount. Neither is better than the other, they are different but they are both computers and do the same things, but they do them differently.