I set the intonation for the new strings yesterday.
Two strings needed minor adjustment. My fat fingers aren't sensitive enough to sound tuneful with guitar strings, especially finer strings like these but I was still getting a sweeter sound with chords above the twelfth.
I didn't touch the nut. @OldG's advice sounds fine. I just don't want to cut the nut until the lad has tried these strings. He might want to go back to the 10s. In either case, I will keep that in mind for further down the line.
His granddad has bought him a stand. He had a wall hanger at the old house but I think that was partly why he dropped the instrument in the first place. It was too much of a stretch for him when he was little.
If nothing else comes of this refurb, it's got his granddad talking about having a another go on his 3/4 classical guitar so I am glad I made the effort.