Keep in mind that the American Revolution occurred in the 1770s while the Napoleonic period began about thirty years later. Fashion changes constantly and we don't expect it to be the same today as it was in 1985. It wasn't an abrupt change from the cocked hat, just a gradual heightening of the crown and a loss of width from the brim to keep proportions attractive. A variety of hat shapes can be found during all time periods, but I'll focus on just the height of the crown to keep it simple.

We tend to expect the wide brims on 1770s hats that obscure the size of the crown, but this portrait of Douglas Hamilton shows a sporting style that makes the crown size visible. A miniature of George IV in 1781/2 gives us another base with which to begin. Fashion plates from 1785-6 show how the crown continues to grow and can sometimes have a slightly more squared off top. A little taller in this plate of 1790. A young French gentleman from 1791. A gentleman from 1795 who has quite a sporting look. And Joseph Wright with his family from 1793. This portrait of James Belcher is from around the time of Napoleon's first reign. It's not terribly different from the the last image a decade earlier.