Well, something tells me if they ever existed, at least one or two must be resting here in Argentina or Uruguay. When the British invaded in 1807, both the Light companies of 88th and 87th engaged in the Battle of Buenos Aires, and somebody must have stolen a their hats as souvenirs.
I'll look around and see what I can find.
Edit: I forgot to add, if the LI wouldn't have that, between 1807-1812, what would they have on their shakos? Big rectangular-ish plate or the hunting horn badge? (assuming they have stovepipe shakos, not belgics)