Can i personally ask a few questions though? What is there was no Secret key? What if i didn't have that piece of paper with those details at all? Would this have been impossible then?
If someone loses the 2FA to their account, then generally the only way to have the account unlocked is contact the exchange and go through their recovery process, which usually involves verifying your ID. If it were any easier than this to remove the 2FA without having access to the account, then the 2FA doesn't provide any additional security, since an attacker could just request for it to be disabled.
If your uncle's accounts are locked with 2FA, and no one can access the 2FA, then your only other option is to contact the exchange in question and provide the legal documents they request as I explained in an earlier post in this thread.
This is all assuming those 16 digit "secret keys" are indeed his 2FA back up codes, but there is nothing else they really could be.
If so, would that generate a new secret key?
You cannot reset his 2FA or generate any new back up codes without first having access to his accounts.