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Tropes Are Flexible, so as long as the main part of the trope is satisfied, there can be some leeway in regards to weapons or fists.
I disagree.
The page is not only referring to "hands on weapons" and "sword counterpart" but it about a specific kind of scene usually done in martial arts media with a final showdown decided by a single strike with the victor being the faster draw. Basically the sword equivalent to quick-draw showdown and frequently involving Iaijutsu
The trope seems to have suffered serious decay and become "any one hit kill using bare hands or a melee weapon" , which is something else entirely.
Edited by shoboniNot really. We already have One-Hit Kill, which you could argue his a sub-trope of.
It even mentions bladed weapons often leading to the Single-Stroke Battle as a sub-type of it.
Edited by shoboniThinking about it, this may be material for a TRS thread about Trope Decay/Misuse
Thinking about it some more, it seems like the basic idea of Single-Stroke Battle is that two combatants charge at each other, there's some audio/visual cue that an attack connected (be we don't know whose), and then everything stops so one fighter can fall over dead/severely wounded/unconscious. That doesn't really seem possible in a fist fight, since a barehanded strike would more likely knock the victim backwards and not allow both parties to continue forward with their momentum, so that after their respective attack attempts, their backs are facing one another.
tl;dr- Feels physically impossible unless done with swords or similar weapons.
System Specs: GPU, CPU, Dell Inspiron laptop, Windows 7 Ultimate 64-bitIf the trope name was changed and the original name was what I suspect it was (You Are Already Dead) then I think i can explain what might be the issue.
You see there is this martial arts manga called Fist of the North Star. "You are already dead" was a phrase from that show (or a translation of a phrase from that show if you want to be specific) that went memetic and became associated with the kind of thing the trope as Ray AP 9 put it was about.
Still under my initial assumption. I can hypothesize that the trope was renamed because of Trope Namer Syndrome. In this case as could be told by the name and focus on martial arts, the trope might had been about the Fist version from the start. However due to other marital art shows following the leader and started applying it to Iajutsu. I can also presume the trope might had been started with both sword and fist in mind and that there was no Trope Decay, but a problem with the description.
Under the later scenario. The trope would not be, and never was, Showdown at High Noon with swords, but instead a distinct trope that covers swords and fists (and presumably Katars and Wolverine Claws as well) that just happened to share a supertrope (One-Hit Kill I presume) and some characteristics with Showdown at High Noon, and therefore the Closest Thing We Got to a Sword Counterpart with that trope
Of course, it all depends on if Single-Stroke Battle and You Are Already Dead are one and the same.
Side note: Turns out Sword Counterpart is a redirect to Gun Counterpart...and a JFF page.
Edit: Turns out my assumptions might had been proven wrong You Are Already Dead is a separate, but still related trope, but I did find another potential supertrope out of it: Time-Delayed Death.
Edited by MorningStar1337Trope Talk, folks. Please use that forum for trope discussion. Thanks!
"For a successful technology, reality must take precedence over public relations, for Nature cannot be fooled." - Richard Feynman

The page itself seems to imply that it's only for swords (citing it as the Sword Counterpart of Showdown at High Noon), but there are some examples of barehanded fights on the page as well.