Maybe it’s worth asking him to assist in person to your repair, so that you don’t leave him with your datas alone. This could be counterproductive for opsec reasons anyway.
I have seen that some of the services that offer data rescue in my country offer just such a service - means that the client is present when rescuing data (which of course means a higher price). Yet even in such a situation, is it possible to be 100% sure that the data is being copied to only one location, and that this person is not doing another secret backup simultaneously?
Of course not. If he will use his computer how can you say that data is not copied somewhere else? You cannot be sure if he do not have som program copying your data elsewhere on the background.
I think that, being on the place while my PC is repaired , I could personally be pretty sure about what's getting on, and being able to spot any fraudulent action.
Just remember that self custody is hard. So you can securely hand over the custody of your assets to a professional custodian (not an exchange).