Hey! NO.
The challenger NEVER EVER EVER, IN ALL OF RECORDED HISTORY, EVER gets to choose the format of the duel.
Never in all of history.
Either they...
• both make their own choices of weapons, or
• there is a set format for duels in society, or
• the person being challenged gets to choose the format.
These are all the basic options of really any society that is able to function for any length of time throughout human history.
I've been researching martial arts as a hobby for about 40 years, and I've actually studied the shit out of this, and it's really some bullshit to see such a rookie-ass mistake in a manga; Japan had a formal dueling code until 1945, so this seems like a really egregious mistake.
Like, duelling was legal when my dad was alive, dude; this isn't hard to get right.
(Countries that allowed the challenger to dictate the terms of a duel invariably fall within a generation or two; think about it)