There are a few things you could do that might help.
See your GP to check for physical reasons for the sore hand when writing - query dyspraxia, hyper mobility, mild cerebral palsy, childhood arthritis and others.
Get eyes checked at Optician if not already done.
Ask school for dyslexia assessment through Educational Psychologist or specialist spld assessor.
Consider paying for a private dyslexia assessment if you can afford it to speed up the process.
It’s going to be difficult to persuade a secondary school to consider lap top use without an official report and specific recommendation. They would need to gather their own evidence to see if your child could write more and achieve higher levels when using a lap top which will take time. After all, a lot of children/parents would “ like” their child to use a lap top if it’s quicker/ easier but exam boards still expect papers to be handwritten unless there is a documented need. Schools have to apply to the exam boards for such special arrangements, providing specific evidence. There would be no point in using a lap top in lessons if exams still have to be handwritten.
Evidence from professional assessments is essential really, it’s not just about being able to use a lap top to write but about knowing why your child struggles so other therapeutic measures can be put in place.
Certainly ask for a transition meeting with the secondary school SENCO in Y6 to express your concerns but you will also need the support of the primary school SENCO at such a meeting.
Have you tried using different styles of pens and used pen grips to see if you can find one your child finds more comfortable?