Breaking the door is a foolish idea.

Throwing it out the window is a bit better, but she would have to take it from Angie first. Then she would have to throw the heavy axe out the window while Angie is out to attack her. If there is any problem, it is in the fact that she refused to hurt Angie numerous times, but that is just her personality. Taking the axe away will not only lower her agility (it did seem quite unwieldy, and Chiko was never strong), it may also force her to use it against someone she does not want to hurt in the heat of battle. Escape was her main priority at that time.

In the end, it is good that she got stuck there for a bit. Otherwise, everyone might have died a bit faster, including Ken.