While I understand and agree with your basic points, I am not anxious to see safety created the way a government like Singapore creates it. One can always trade freedom for perceived safety, but it rarely ends well.
It is an unfortunate fact of our culture that violence in the streets is a real exposure, so both men and women need to be prepared to protect themselves. So, yes, women should carry Mace or Tasers and learn self defense because one way to feel less of a victim is to have the tools to protect yourself. This doesn’t remove from men the obligation to stop abusing, but it does help remove the stereotype of woman as victim.
The Women’s march was important because it is part of this same process of ending the victimization of women by refusing to be quietly victimized. I hope that women and their partners keep marching. I also hope that the march(es) are recognized as a demand for rights owed, not simply a protest against Trump.