I would think it would be the opposite. As a man I would do everything I could to avoid using a gun on an unarmed person if it was only myself that I was protecting but in most cases women aren't as physically strong or quick as males so in many cases they could be physically overwhelmed if only using a blade. Out of the women I've taught how to shoot & basic aspects of self defense with a firearm fortunately none have had to pull the trigger however there was one that had her car blocked in, she immediately drew her handgun, pointed it at the guy, told him to get away from her car. She later told me that she was prepared to pull the trigger if he hadn't backed away & had instead hit her window again as if he were trying to break through.
There are exceptions though of course. My grandfather's wife used to keep a butcher knife next to her bed when my grandfather was out of town, even though there were guns in the house & she knew how to use them.