This is a tricky question that somewhat depends on how you define 'duel'. In a non-battle situation the duel is the entire reason the two samurai are fighting; without the duel challenge, they're still just calling each other honorless pig-dogs.
On the battlefield, the samurai are already trying to kill each other. So what makes the fight become a duel? A couple options, not mutually exclusive:
- The fight becomes personal for some reason; the two samurai perhaps know and hate each other and have personal grudge to settle.
- Two significant figures (say the commanders of the opposing sides) happen to find themselves next to each other and formality is thus called for; the fight becomes a duel for the simple reason of assuming duel protocol.
If #2 is true, then by definition (unless, you know, Crab) it would be fought with katana. If only #1 is true, then the 'duel' may consist entirely of a shouted challenge before continuing the ongoing attempt to kill each other.
The difference would likely be in the eye of the spectator; if the samurai lay down their battle weapons and assume iaijutsu stance, then everyone's going to know they're dueling. If they just shout the challenges, maybe only they consider themselves to be dueling.
The honor level of battlefield dueling with non-katana should also be considered in the context of armor. Outside battle duels are not fought in armor, but in battle it's extremely impractical to remove one's armor and then find a way to get it back on after winning the duel. So honor standards are going to be different than for non-battle duels.
In the end 'allowed' might not be the right term. I'd consider the attitudes of the observers when determining how the characters' circumstances change as a result of the duel. Different observers care about formality to different degrees. If it's a Crab v Mantis battle, no one may care.