Things are shaping up nicely...
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The sword appears to be a traditional, katana/oniyuri style sword similar to the Dragon Sword.
The blade is normally seen being held in a scabbard on Hayate's back. Hayate has been seen using it in battle during the conflict against DOATEC in Dead or Alive 4 and Dead or Alive 5.
In Ninja Gaiden 3 Razor's Edge, when Ryu Hayabusa obtains the Blade of the Archfiend and the ability to use the dual katana style, he uses Jinran-Maru in his left hand as his secondary blade. It can be concurred that the sword may be imbued with with the power of the wind as with his ultimate technique, after the flurry of slashes, Hayabusa sends out three wind blades (four if you count the last cross-slash as two).
This is only speculation though, seeing as the wind blades are sent out from both Jinran-Maru and the Blade of the Archfiend.
Ninja Gaiden IIIEdit
When Hayabusa traveled to Rub'al Khali, he managed to destroy some LOA Terrorists' Motorbikes with a Lock-on Bow, as the Dragon Sword was in his arm due to the Grip of Murder casted by the Regent of the Mask. Hayate, upon hearing this news, sent Ayane to Rub'al Khali to let Hayabusa borrow his Jinran-Maru. She told Hayabusa to bring it back in one piece since it's a loaner. Hayabusa uses the Jinran-Maru until his return to the Hayabusa Village to acquire the Blade of the Archfiend.