We'll get one thing out the way, nice and early; in many cases, there is no need for the raccoon that is proving to be your biggest pest, to die. There are various methods of raccoon removal that you could put your faith into before ending the life of an animal that might not require such forceful treatment. Did you know, for example, that exclusion devices (one-way doors) with raccoon eviction fluid can actually be quite an effective combination when dealing with a female raccoon and a den full of kits?
Killing the animal, in some cases, IS the most humane ending. Released animals will rarely have an easy time of things, especially if they were injured or never really capable of living in a rural setting in the first place. A raccoon that has been born into — and has only ever seen — urban habitats won't have the first clue what to do when it gets out in the wild, with real and big predators that don't really dare to come to town much.
If you were to pass a raccoon in a live cage trap over to a wildlife rehabilitator, one of two things would happen. That animal would either be given the once-over by a vet or other animal medial professional, and then released back into the wild. This 'wild spot' will need to be researched, and then permission must be granted from the landowner before the raccoon can actually be released. In places where this practice is legal, some landowners may have relationships set up with wildlife rehabilitators, offering a humane approach for all parties involved.
If a raccoon were to be sick or injured when it was captured, it would have very little chance of survival in the wild. Many wildlife rehabilitators (and even volunteers) do not have the resources to nurse these creatures back to health, especially with their rabies status, and vet bills for such a thing would be into the thousands, perhaps even more than that. The most humane ending in this case would be to destroy the animal, using a carbon dioxide chamber. In most states, this is one of the only legal ways to put down a wild raccoon.
You could look at shooting the raccoon in a cage, but you'd need to be a pretty good shot if you're looking at shooting a wild raccoon you haven't even caught yet. To be frank, you'd still need to be a pretty decent shot to kill a raccoon in one go. It will move around in that cage like something possessed, more movement and noise coming with increased stress levels. A large enough cage could cause the animal to throw itself around so much, it has the room to cause serious injury. You will also need to have a good look into local firearms laws to make sure you're not putting yourself in danger of facing jail time.
Poison isn't an option for raccoons. It doesn't work, mostly because there isn't actually a kind of poison that you can buy that has been shown to work, or be legal for, wild raccoons. If you plan on using poisons that are designed for other animals, such as rodenticides, you must be aware of the very serious dangers to life you are sending out into the world. You would need a much larger dose for a raccoon than you would with a rat, and that high a dose has the potential to not just make another animal or person (child) sick, but kill them. That would then be on your hands.
For more information, you may want to click on one of these guides that I wrote:
How much does raccoon removal cost? - get the lowdown on prices.
How to get rid of raccoons - my main raccoon removal info guide.
Example raccoon trapping photographs - get do-it-yourself ideas.
Raccoon job blog - learn from great examples of raccoon jobs I've done.
Raccoons in the attic - what to do to solve the problem.