I've done some counting of how and where bâtons appear:

• Total bâtons: 18
• Bâtons in the possession of men: 6
• Of those 6, 3 are actively being used on women.
• Bâtons in the possession of women: 12
• Of those 12, 7 are actively being used on men.

In other words, this weapon is shown in the possession of women, and being wielded as a weapon by women, twice as frequently as it's shown in male hands.