Horsehead pommels go back much farther than the early 1800's - to at least the Romans here's just one such Roman Pommel:
http://www.time-lines.co.uk/roman-horsehead-dagger-pommel-015226-26501-0.htmlThey appear world wide, especially popular in India and the Middle East and other horse "cultures"
As for the half horse half alligator line, Jim Bowie would have been a Johnny come lately to the term. The first published usage that I know of was Samuel Woodworth's "The Hunter's of Kentucky" written in 1812 -
http://www.contemplator.com/america/hunter.html.
It became the campaign song for Andy Jackson's presidential run.
Mike Fink, was one of the most famous to apply the term to himself and it was a term often applied to the rough and ready river boatmen and other frontier types of the early 1800s, including:
"I'm half-horse, half-alligator and a little attached with snapping turtle." - Davy Crockett
The halfhorse/half gator pommels on the other hand, most often seen on Sheffield bowies, are definitely post Mr. Bowie and the infamous Sandbar fight. Sheffield knives ran the gamut from excellent to bad with many knockoffs - in terms of today, think quality factory made knives such as Gerber/Buck, etc. and then the el cheapo knockoffs from China and Pakistan........
BTW - there's a much larger picture of that oversize folder with the tortoise shell grips in Flayderman's "The Bowie Knife" - folders like these are always interesting but I often wonder just how usable some/many were - but then again the "coolness" factor has always been part of the human race.......