The numbers of original U.S. swords with ivory play against the odds of finding one in reasonable condition for uniform wear, if that was purpose. Aside from the orders from Birmingham in the first half of the 19th century, you will likely find none. There was a period of that century where the mameluke was dropped and by the time it was adopted again, celluloid and other plastics were the way to go. I should pull a couple of titles here instead of guessing at dates but from roughly the 1850s to the 1870s, the mamelukes had been replaced by what is now your marine nco sabre. Previous to the 1850 foot officer variant being assigned to the ncos, that was the marine officer's sword and the ncos (from 1840-1870s) carried swords similar to the the army's 1840 sergeant's spadroon. On going back to the mameluke for officers, it was felt the ncos deserved an upgrade from the simpler straight spadroon.
At any rate, if looking for a collectible, it will be a matter of catch as catch can and as mentioned, a pretty rare find at this point. The British 1831s are plentiful and most through the 20th century will be ivory (typically $1500 and up these days). I was just reading hard numbers for mamelukes contracted from Birmingham when first officially adopted by the U.S. but am not recalling where I saw that. I'm sure I was tracking something else at the time. There are several good web pages on Marine uniform and sword regulation going right back to the beginnings. It is that early break in regulation and that England controlled the ivory trade that makes the use of the material on American swords less common than one might think. Post American Civil War, almost unheard of.
Cheers
GC