No expert here, but for most simple things (safety harnessing, knife usage, etc.) we did not have a controlled "safety document" for each...though we did have some level of safety training for proper safe usage.
For specific things like fire extinguishers on metal fires we did have a specific document. Not that the doc had much play if there was a fire, but it was something to log training against more than anything. The doc itself was bounced off of hazmat firefighters and the local department.
Is there a specific safety concern that you are looking into?