Is “Black Whirlwind Li Kui wielded double axes, was rash in temperament, and was a leader of the Liangshan infantry, often saying 'Kill our way to the Eastern Capital and seize that bird's throne.'” true?

The records of the Song Shi in the biographies of Hou Meng and Zhang Shuye regarding the uprising of Song Jiang are extremely brief, merely stating 'Song Jiang and his thirty-six men ran rampant in Qi and Wei.' Although the name Li Kui appears in the 'Da Song Xuanhe Yishi' (Anecdotes of the Xuanhe Era of the Great Song) compiled in the early Southern Song, there is no detailed description of him wielding double axes, killing like a butcher, bloodthirsty, or loyal. This rough image of Li Kui was gradually accumulated and fictionalized through folk storytelling and zaju (variety plays) from the Southern Song to the Yuan dynasty, and is not the historical reality.