If we allow ourselves to think "out of the box" on this subject -
A number of other societies and cultures continue to field long knives / swords on the battlefield. And U.S. forces have had to contend with facing such weaponry as a physical threat (Haiti, Africa, Afghanistan, Somalia, Columbia, El Salvador, for example).
SF operators routinely work in areas where edged weapons of this type are available and used, some as everyday instruments (machetes), and others as weapons (sole purpose).
In El Salvador both government and guerrilla forces routinely carried and would use short combat machetes.
Current CQB programs for our own armed forces, as well as foreign forces of an elite nature, train in the use of shovels, machetes, knives, and other "cold" weapons...to include in the appropriate culture - swords.
I learned of at least one recon Marine during the gulf war who carried a Hartsfield "Waki" in a over the shoulder/back scabbard. Once in country and under fire it's darned amazing what "special" personally owned weapons come out of the seabags and rucksacks!
Personally I like the tomahawk (LaGana)for a personal cold weapon in the military environment. In Kosovo, Albanian guerrillas commonly carry a traditional Albanian hatchet as part of their combat equipment. Have one. Wouldn't want to get whacked with it
A solid, simple, well built short sword in a kydex scabbard with shoulder carry system remains a great weapon IF you know how to use it well enough to get the job done.
I believe the Mineral Mountain (?) guys make such a sword, as do some other working cutlery folks.
And there's a lot to be said for a $5 machete with a keen edge...