It sounds like you should have a QC manager review the records generated by the QC tests that currently release the product and sign off on it.
In my position, I review the 'daily paperwork' as we call it informally, which includes production documenting lot codes, product weights, pre-op inspections, as well as receiving and shipping documents (temperature control, cleanliness, and security), temperature monitoring logs, and quality inspection reports. I assemble them all into a 4-6" packet with a cover page I made where I check off the documents in the packet I'm signing off on. It's not really pretty but it does ensure that a senior QC person is reviewing the paperwork and makes it really easy to find what you're looking for if you ever want to go back and look in your records. They're all together and dated and sorted.