If you do decide to take your ds out of school for the last two weeks you just need a simple letter to deregister him. There is no need to give any information about how he is to be educated in the future.
We took ds1 out from year 5 for nearly the whole year (aspergers and not a good school to accommodate it) and ds4 out for two weeks after a house move, the new school had a place for him but had to wait 28 days after trying to contact a different parent to give them the place before offering it to us. Dh had started a new job so couldn't drive ds to the rural school he was in so he had an extended Easter holiday! (Which he loved.)
The basics of the letter were:
Dear head teacher,
As of xx/xx/xxxx date we are removing "ds' name" from Xxxxxxxxxx school to be otherwise educated. Please remove him from your registration as of this date.
Yours X. Xxxxxxxxx.
You can pad it out so it doesn't come across as too sterile, and we put a sentence at the end thanking them for all they had done in educating the boys too. (Didn't particularly mean it for ds1's school, but did for ds4's. They also lost me as a member of staff at the same time!)
You don't need to give any other reason than 'educated otherwise' and don't need to explain yourself. It is up to the LEA to investigate whether or not your ds is being educated and since he is being registered at another school for the next school year there will be nothing for them to do anyway.
When we deregistered ds1 it looked like a weight had been lifted off his shoulders and he started smiling. He went to a lovely school for year 6, did well in his SATS, did extremely well in his GCSEs and is now awaiting his A Level results, so having a relaxed year 5 with museum visits instead of institutionalized learning did him the world of good.
In your situation if you need to remove ds from school for the last two weeks it would be easier to officially remove him rather than going off sick, this will remove the chances of someone picking up on it and asking you to prove he is unwell. (It would be stupid of someone to do that but there are jobs worth people out there.) Deregistering your ds would mean less hassle and not risking the possibility of a fine for non attendance. IMHO it would be the easiest option, no hassle and taking a legal route. After all, if he is absent for illness because of stress then it is harder to prove that than being able to show evidence of a physical illness.
Hope all goes well and your ds enjoys his new school