How far along are you in the legal process to sell?
As I’m sure you’re aware, once contracts are exchanged they Are committed to the purchase, do they have any plan to revisit the property prior to exchange? If not then, as you say, with no planning permission required I can’t see how they find out about it.
If you wanted to be really sly about it you could ask the neighbour to delay anything visible until you’ve exchanged contracts possibly?
Also, whilst he may not need planning permission to build it that doesn’t necessarily mean it’s legally compliant. Are you aware of any covenants in the Transfer - for one thing if he builds windows on the side of the building which is on your boundary then there could be a privacy issue. There’s also the thing that if the fence is jointly owned by you both then I can’t see how he can pull it down without your consent.