We use Lincoln and its easy to get C of C's. We also use ESAB, and I have to get them from my salesman, but again we buy so much I have it within 2 hrs.
Before you buy the electrode, make sure that you can get one or don't buy that product, pick another manufacturer. Especially don't go to Harbor Freight and expect them to give you any type of paperwork on their electrodes.
When dealing with traceability issues, a good auditor will not accept anything less than a melt certificate from the manufacturer, traceable to the purchasing document and to the shop order where the work was performed, showing that heat number (aka melt no., lot no., etc) on each document in turn. If one of your welds fails and you cannot show this traceability, you are very likely going to be liable for the consequences of that failure, especially in aerospace. I can only guess at some of the difficulties you have been experiencing; flag-tagging, traceability, availability of smaller quantities, proper unit packaging and identification to name a few. You will find, as did I, that you have to reach out for suppliers. Every order I make is out of state. I can PM you with more info, if you want it.