the left appears, hopelessly, the dominant sword arm(the bokutō[japanese wooden sword] is a focus weapon/discipline). peculiar, being right handed in absolutely everything else... including the practice of other stick weapons. also, kind of peculiar in that a samurai likely would not have been well received in using left handed swordsmanship, and it'd probably be seen as utilizing an underhanded method that others had not trained to fight/read.
in attempt to look it up, there are made mentions of niten ichi-ryū(devised by a rōnin) to justify left handedness, but dual swordsmanship still relies upon a daitō/longsword in the right, and shōtō/short-sword in the left, so the saya/scabbards would have been positioned in the same fashion as a right handed swordsman(tapping another's sword was supposedly a challenge to the death, along with many other bizarre and seemingly innocuous actions... so to fashion them to the left and pass another with their's fashioned to the right, could have been quite precarious), and it's a technique that does not use the swords in the same fashion... it's as if they're handled as entirely different weapons used for swiftly outmaneuvering and locking an opponent's blade while flaying their vulnerable points instead of cutting deep... so the justification is about as questionable as if to compare the samurai's sword etiquette to the foot-soldier's yari/spear. even if to gain the strength and discipline to cut deep with a sword in each hand, it would be a wasted effort beyond training for strength, because two hands to one sword would be vastly superior for draw and cut with that kind of strength and control.
probably over thinking things a little... especially in having no desire to even hold an actual blade.
_________________
七転び八起き