Most of the answers so far have focused on using some type of radiation to kill your target (since it's been established that projectile weapons are a non-starter). However, there are some problems:
- Microwaves are stopped by even thin metal (e.g. your microwave oven doesn't roast you every time you use it). They also have a long wavelength (on the order of 10 cm), so you need a large emitter to create a focused beam; a handgun-sized microwave weapon would spray radiation indiscriminately.
- Going to shorter wavelengths doesn't help. Terahertz radiation doesn't penetrate objects very well (the body scanners used by the TSA can see through normal clothes, but that's about it). Many answers suggested going even higher to x-rays. However, low-energy x-rays are stopped by things like pieces of paper and air. High-energy x-rays pass right through your body (which is why they're useful for medical imaging), so they violate the "no collats" requirement. There is no intermediate range where x-rays penetrate walls but not tissue. (This is because humans are made of low-Z elements: hydrogen, oxygen, carbon, and nitrogen.)
With projectiles and radiation pretty much discounted, that leaves only one weapon left: information.
There are two scenarios I have in mind.
Nanobots, Nanobots Everywhere
Typically I don't like to lean on the crutch of nanotechnology, but it fits pretty well here. Imagine a future where invisible nanomachines cover every surface, fill the air, and even our bodies. They do a lot of amazing things, like turn every surface into a microphone and touchscreen display, constantly analyze the air for contaminants and monitor weather patterns, and continuously repair our bodies.
However, one organization has turned the system against us. Whether it's the government building backdoors into the system, or a group of industrious blackhats, someone has a way to override the nanomachines' programming. They now have thousands of ways to kill you, from reversing the nanomachines that increase your blood oxygen and endurance so that they asphyixiate you, to instructing the brain-machine interface nanomachines to kill all your brain activity. They can even make it look like a natural death or an accident, and when the override is wiped from the nanomachines' memories, no one will be the wiser.
Mark of the Beast
And he causeth all, both small and great, rich and poor, free and bond, to receive a mark in their right hand...
In a less technologically-advanced (but perhaps more dystopian) future, the government might require everyone to get 'chipped' with an ID tag. It's a great convenience, since you no longer have to carry around your ID, worry about getting it lost or stolen, or renewing it when it expires. Maybe it even functions as your credit cards, ID badge, passwords, and more; it might even be voluntary but ubiquitous, like cell phones.
Once again, someone has backdoor access to the system, and has found a way to kill you using your chip. This could be a secret feature placed there by the government, The Corporations, or a supervillain blackmailing the designer. It could also be a simple design flaw: when overloaded in a certain way, the fried chip releases a toxin into the bloodstream, or creates a destructive feedback loop in the nervous system.
The method of death can be as subtle or obvious as you like. It may be clear that the target was killed by their 'malfunctioning' ID implant, but without comprehensive logs determining who killed the target may be impossible.
In both of these scenarios, the 'gun' merely acts as a target designator, like the scariest point-and-click interface ever. The
great scary thing about this system is that is scales perfectly. An aspiring neo-Nazi could use the system to kill anyone whose DNA he doesn't like, or a supervillain could hold the entire planet hostage without raising a weapon.
Of course, the most thought-provoking part of this question for me is, why would police need to be issued untraceable weapons? (!!!)