hopefully pretty quick demise
Yes, that is the risk. Will it be painless? For me it's too much of a risk - imagine wounding or maiming the animal? I'd rather not take the chance. [1] How could one sleep at night, knowing there was an animal with a festering wound, or left to die a slow death, because of human error re. the weapon used to kill the animal? [2] Apart from the risk of wounding or maiming an animal, how do you know you're not depriving a baby animal of its mother? How could one sleep at night, knowing there was a baby animal out there in distress, or left to die, because I'd exercised my 'dominion' to do whatever I want with the animals on the planet? What gives me the right?! [3] Finally, living in a modern liberal democracy, how could I be sure that I was killing the animal for food/nutrients and not unconsciously indulging my base emotions to prevail over the death of another living being and so reassure myself of my own survival fitness or superior worth on the planet? There is nothing about my life that makes it superior to that of an animal's; we are the same. If anything, animals have the moral high-ground, overall. Generally speaking, humans have a greater desire for power, control and dominance.
Animals already suffer too much on this planet at the hands of humans - from pollution to encroachment on their environments and butchering of their ecosystems. To willfully inflict harm (let alone death) on an animal standing in front of me I find unconscionable.
My rule is: would we do it to a fellow human or a child? If not, don't do it to an animal - the Golden Rule of "Do unto others as you would have them do unto you". It just seems too convenient for humans to say that that applies to everyone except animals - everything interpreted in the human's favour! That doesn't show great perspective-taking or empathy.
I am aware of arguments from 'Fast Food Nation' and such that hunting is more humane than animal farming (I like your comparison with holocaust conditions), and the hidden costs of vegetarianism. It also took me years to stop eating meat but one day the tipping point was reached and I just couldn't justify prioritising my own palate over the suffering of a sentient animals with eyes and nose and mouth --- everything about it designed to help it survive - just like humans.
I'm not in favour of arguments that (1) animals do it therefore we can do it; (2) humans have always done it therefore it's OK to continue doing it. There are too many counterexamples and inconsistencies for those two justifications to apply. To name a few. (1) As Streetwise says, animals need to hunt for food - they don't have bank accounts; in today's society humans don't need to hunt for food. (2) There are many things humans did in the past which applied reasoning revealed to be barbaric, misguided or insane e.g., throwing raw sewerage into the open street, beheading political adversaries, child labour, child capital punishment, labotomies, devaluing women, enslaving ethnic minorities. Just because we did something in the past does mean we should continue - we can still apply our enhanced thinking abilities, changed socio-economic circumstances and improved awareness to do things differently.
I concede that even monkeys are omnivores and are known to eat a mouse or locust occasionally. If there is any argument for eating animals, it should be as humane as possible (cameras in abattoirs), minimal transportation (
Compassion in World Farming | Compassion in World Farming), higher prices (people value dirt-cheap meat without caring or being curious about the condition the animal's had to live in), and it should not be eaten often - maybe just a couple of times as year - way less than many societies of the world are currently consuming (e.g., cheap meat and chicken in a daily basis). I like what 'David Fisher' did in 'Six Feet Under' when they had meat for dinner. While saying grace, he thanked the animal for sacrificing its life for them. Not sure how much informed consent was involved from the animal but it was a nice sentiment - better than no acknowledgement.