They make it nearly impossible to get a license to carry a gun in NYC. You can get a license for home protection, but the gun isn't going to help you on the street.

You basically have to incorporate yourself, and describe why you - as a business entity, need to defend yourself. You'll need to include a letter of necessity, which looks for things like - the nature of your business, and some business records.
- the reason why you need a gun for protection
- details about your place of business, and their agreement that you can carry a gun on the premises.
- while training isn't legally mandated, NYC wants you to have it and prove it.
- your plan for where the gun is securely stored when you aren't actively using it.
- your understanding of the laws regarding gun ownership, lawful carry, and the use of force.
- if you've ever been the victim of violent crime, they want to know about it.

The full letter in on page 3 of the application.

Keep in mind that NYC laws are pretty restrictive, too, especially outside the premises of your home or your own business.
You can't pull your gun because you think someone might slash you, or might be carrying acid. You have to believe that the threat is imminent.
After they do slash or splash you (or someone else), you don't get a free pass to draw on them, or shoot. If they run away, or drop the weapon, then you/the victim aren't in any further danger.
You basically have to have a reasonable belief that an attacker is about to kill/maim/seriously injure you or someone else, and that shooting them is the only possible way to avert that.
You don't really get to warn them, shoot a warning shot, or tell them you're going to shoot. If you have all that time, then the danger wasn't really that imminent, and you can be sued/prosecuted for your actions.