The harness, container, and canopy would each have a label with the model and serial numbers. Those numbers should also be recorded in the rigger's rigging log book and on the packing card. Whether they all actually are on the card would depend on the thoroughness of the rigger. The canopy info should certainly be.
I'm not an expert on the 302's or the specific information flow in this case. But the following is what I seem to remember from reading it here.
The 'lost in the mail' info you refer to refers to Cossey's log book info. Supposedly Cossey claimed to have provided copies of it, but the FBI doesn't seem to have it. The cards were both on the plane. I don't remember if the full info on the harness/containers were on them, but the canopy info, including serial numbers, were. I think the NB6 container has been debunked. That would have been Cossey's personal rig that he originally had claimed to provide, but he may not have. I think the two back chutes actually provided to Cooper were determined to be Norm Hayden's bailout rigs, which were older containers that had had newer harnesses installed.
You should be able to find all this info in Flyjack's posts in this very thread.