For a straight razor, there are some martial arts that still have that as one of their weapons -- the old style of Savate and Capoeira are the ones that come to mind but there may be others. Blades like the Spyderco one have short heavy blades, but they are broad enough that I wouldn't discount stabbing since that's often a prelude to tearing a wound open anyway.
As a primary melee weapon that isn't likely to draw unwanted attention, I have a cane for that.
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traumabrew The problem is that by the end of your post, you've pretty well said there is no self defense. Even for firearms, you go through a long discussion about carrying a firearm, but as you said -- people don't always go down or at least may not go down before you get hurt. Sixteen hits with 9mm hollow point shows what can go wrong.
The points you have raised are valid in some cases, but using self defense courses as an example, it is better to have some options than no options at all. A self defense course isn't 20 years of training in a martial art, but it doesn't really take that to learn how to bring your heel down on the arch of someone's foot. Steel toed boots aren't much protection from that; some people wear steel toed boots, so knowing to stomp to the top of the foot instead of the toes can make a difference and even someone too high to feel it doesn't chase you quite as well with a broken foot. Similarly, not everyone starts as an attacker. But a date gone wrong or a disagreement with someone can escalate. Knowing how to use your legs and leverage to get out of something like a wrist grab is better than nothing and again it doesn't take a lot of very complicated training. Fold fingers over, strike to the throat, stomp to the top of the foot, get to a safe place, call emergency services -- more complicated but if someone tries to choke you it is once again a better option than the reflex to claw at someone.
Keep the car doors locked, don't stop for strangers, park in well lit areas, observe the area before getting out of your car or leaving the building -- those things are also part of a self defense course, but the other stuff is for an option if you find yourself in a situation that needs it.