Yes I have.  Got some photos somewhere. The scraper wads appear to be of some metal looking like zinc with a composition wad between the metal wads.

The Westley Richards Cartridges had the wad glued to the base, were then dipped in hot wax at the bullet end for the length of the bullet, they were then wrapped with the cover (which had a cloth tear strip to facilitate its removal).  
 
 Assuming the similarities of this to the Whitworth, it would be a case to say the the outer cover went over the base wad as well, practicalities of transport & contamination would make it virtually essential.  So I'd say your interpretation is correct.
Adrian.

I have two original monkey-tail cartridges, one complete with its outer wrapping and tear off ribbon, the other without the outer wrapping.
 
As for the Whitworth, I have a copy of the original cartridge for the Enfield Whitworth Pattern 1863 which shows that the outer case to be torn off was only half the length of the complete cartridge and covered the bullet paper and the grease wad. The interesting thing about this cartridge was the "Stop Band" which was located immediately adjacent to the tear off outer wrap.  When the wrap was removed this thick band was located so that as the cartridge was inserted into the muzzle it came to a stop against the muzzle thus locating the bullet at exactly the right depth. It also assistd the motion of breaking off the cartridge paper prior to ramming.  It is by far the most complicated of the paper cartridges of the day and therefore expensive.