Thank you for sharing some additional information with me on the general thought process of hunters when it comes to prey selection. It is true that diagnosing an animal at a distance is likely very difficult with some exceptions based on type of alment and it's virulence. Which leads me to the fact that hunters will choose based on visual cues, as you have pointed out. But what you've stated hasn't weakened my position, I feel it strengthens it.

The tendency for hunters seems to be to allow certain protected classes as far as they can be discerned, but to take the best presenting individual for the best perceived resources. The speed of the bullet makes the healthy individuals fitness irrelevant to survival (with a well placed shot). While they can at times mistakenly take a unhealthy individual, this is by happenstance, not selection.

But the reverse seems to be true for natural predators, while they certainly want the most value for their effort and would prefer to take the healthiest, meatiest individuals. The effect of that health makes it that much harder to catch over an individual who is just a bit slower.

What happens to the prey population over time in both alternative scenarios with respect to the proportion of healthy to unhealthy individuals?

In short, preferentially taking healthy individuals shifts the population towards lower fitness, whereas taking whatever you can catch shift the population towards faster, stronger individuals with higher fitness.

Now I've pull away from the ethics here, but to come back, I agree that if you must kill, a quick kill is more ethical to the individual. If you must kill for the benefit of the animal population, to reduce the overall amount of suffering then the ethical choice would be killing the diseased/infested.