Before SHTF, it will depend highly on your local laws (and your willingness to abide by those laws . . . or not). Certain slingshots can be very concealable and are pretty deadly. Ammo is pretty easy to find as well. Rocks, marbles, steel bearings. There are some pretty nifty self defense canes out there on the market and so long as you look like you need that cane, no one is really going to look much close. There are always knives that are within the legal size to be carried and are throw-able by design.
After SHTF, it will depend on the situation and what you need the weapon for. But there are many options. Various bows, axes, knives, machetes, short swords, long swords, spears, pikes, sword & shield, atlatl, staff, war clubs, war hammers, flame thrower.
If you are a crafty enough person, you could make some of this yourself given the time and resources. Relief springs in vehicles are an excellent source of metal for knives/swords. Homemade flame throwers are pretty dang scary . . . no one wants to burn to death.