With a couple of exceptions, anything that I might need for an audit, I keep locally in a lockable filing cabinet within our office area and/or its stored electronically on a local (virtual) drive that is limited to specific persons and is backed up by IT hourly with off-site disaster recovery in place. The exceptions are cases where the "paperwork" is me adding food safety practices into other processes for efficiency such as adding language to the driver's logs for FSMA (U.S. law) which are stored with the shipping info. I can do that because we have a good overall document retention policy in place. Our audit scheme mandates two years for document storage, our internal policy is three years unless something overrides it (like SDS). I've tried to make all of my processes easier than what was in place prior. That allows me to avoid the "I'm too busy" excuse for not keeping up with the paperwork.
For my receiving log, I use a large label that goes on to the back of the each BOL and is filled out by our receiving manager. That was easier and cleaner than a separate log. Streamlined the receiving process, meets our audit scheme's requirements and I am comfortable that we have a good process for storing those records. Accounting scans in all of the BOLs, so we have them as needed for audits. Because we have the records, I don't worry about them being stored elsewhere. If I didn't trust that was occurring, I would insist on having a copy for food safety records. You are the one that will bear the brunt of the criticism if paperwork is missing during an audit, so most of us are pack rats.
I am trying to move more and more records to electronic since it makes the process of managing easier.
Anyway, not sure if all of this helps. Good luck.