No. Your child would be better off getting ot and physio input for his dyspraxia (did they not test for add/ ADHD when they did the iq testing?) so that he is able to record his knowledge and ability and have it recognised.
A private school would possibly be the worst place for him until he has the basics of recording figured out one way or another, either via ot support for pen,a ship, including the use of writing slope/ seating wedge/ pencil grips as required, handwriting course (write from the start or similar).
Private schools generally are not enormously supportive of sn that requires intervention, unless the parents are going to pay for it. In which case move schools and pay for the ot and physio support.
If he has a bursary, then you may be ale to pay for the therapy support that will help him - if not, I would probably suggest getting the therapy in first, letting him work out a method of recording (even if it is laptop) and then moving him.
I am all for extension and challenge for more able pupils, but for some reason your child is not performing academically. I suspect this is due to dyspraxia and recording issues, but you will need to be entirely upfront that he is not currently performing academically, and ask how the new school would deal. Otherwise you run the risk of them withdrawing the bursary when the promised genius doesn't deliver, and having to move him back.
Have you been upfront with the new school that he is currently performing well below average? Presumably because of his disability?