Firstly, apologies for not giving a definitive answer.
Technically speaking, each country has its own individual customs clearance regulations so you would need to check in an international trade procedures guide such as Tates or Croners to see if original export documentation was required to enable clearance.
Logically speaking if shipping under Letter of Credit the originals are normally called for as part of the presentation, so it would be impossible to send the originals with the goods unless you wanted to be discrepant against the LC.
Speaking from (bitter) experience I personally would always send the original with the goods if possible. When shipping via seafreight I will courier the export docs to the customer in advance so they can present originals for clearance. I always send a scan via email to my forwarder (or the customers forwarder for EXW shipments), the forward will normally pass this on to the local/clearing agent.
The EC CofO is a three page set, the chamber will retain the pink, leaving you with the white and yellow copy. You can normally get additional yellow copies from your Chamber of Commerce free of charge, some local Chambers may apply a nominal fee. I get at least four additional yellow copies and provide one to all relevant parties.
I hope this helps!