As long as you submit those KYC documents in a safe and trusted crypto exchange in your country I believe that you have nothing to worry about unless it is about hacks.
How can you possibly know if an exchange can be "trusted" or not? It only becomes apparent that they are untrustworthy after all your documents have been leaked across the internet and sold on the dark web. You have absolutely no idea how many people at the exchange will have access to your documents, who those people are, how they were hired, if they have had any kind of background checks done, etc. You have absolutely no idea how many people are working for the various third party contractors, data processors, advertisers, etc. which the exchange will search your information, or their backgrounds, etc. You have no idea what kind of security system the exchange have in place, how they secure the KYC database, how they monitor access to it, how they transfer it to third parties, etc.
An exchange can look all bells and whistles on the outside, and yet still leak or sell your documents (e.g. Binance and Coinbase).
The only safe KYC is no KYC.