I found some more reference that pretty much agrees with every thing you've done. A realy good contempory picture but it must have been late in 1815 because the honours "Peninsul" and "Waterloo" have been added to the sabretache. I forgot about Chas Stadden's book on The Life Guards that was published by Almark in 1971 (although he does show a red edging to the black sheepskin!
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The word Corporal was used in the Household Cavalry instead of the word Sergeant. Until the rest of the army adopted the rank of corporal in 1878 when the Household Cavalry rank became Corporal of Horse. The badge of rank is three gold stripes with a crown above, I believe this is the badge Corporal Shaw would have worn. We still don't have sergeants.
Also here's that helmet. It's been gathering dust in the loft since 1995. I've added one of my 32nd figures for size (I.G. wolfhound 1900) I can't find the scales or rosettes at the moment. The crest doesn't assemble properly because I had to add bits for the moulding process.
Obviously I had to be careful with the original helmet while I was handling it, so I used the "brass rubbing" method to get the sizes and details. I had to enlarge the helmet because the original would only fit a modern child! That was the only alteration I made though, I stuck to all other measures.
Martin