100 years ago puts us back to 1905. US Horse mounted calvery had yet to be disbanded, and would have still been issued saber. Patton himself designed and had accepted a replacement saber after your 100 year cut-off.
While we can argue the releavance of horse calvery of that era on the contemporary battlefield against first rate powers, it did still have some life left in policing actions in mexico and the rest of south america.
If you wish to be a bit more broad in your definitions, several british units never gave up the kurki which is at its longer lengths, nothing more than a reverse-curved short sword.
I would agree that long-swords have become irrelevant militarily except as status symbols since about 80 years ago. Oddly, they might well be better suited for civilian carry than handguns. They'd offer a better visual deterant, are just as effective within ranges accepted for self-defense (15 feet or so), and could even be quicker to deploy. While not offering the same force-multiplication as firearms, they can come mighty close.
In any event, I would never claim them to be un-American. From the farmer/volunteer at bunker hill with his brass hilted short sword, to the privateers cutlass in 1812 all the way up to the calvery saber that chased Pancho Villa. While not distinctly american, I wouldn't claim they were un-American.
If you have evidence of the resurfacing of the hatchet prior to the 1960's, I'd be interested in hearing it. The most common re-adoption of the axe that I am aware of was after the partial disposal of what displaced the sword to most infantry. Namely, that pole-arm also known as a rifle with bayonet. Obviously the AK series is on the short side for most bayonet maneuvers, and the AR/M16 platform is of questionable durability when used as a club.
I doubt that a short, thrusting sword is any less appropriate than the modern hatchets. However only one of these has utility besides as weapon, making it worth humping. It may well be interesting to see as more militaries begin issuing balastic armor if the hatchets persist. While a hatchets larger brother is well suited to defeating such, the smaller versions lack in point penetrating power as do handgun rounds. If this comes to pass, then moderate length thrusting swords could once again be of service.
