When there is an intrinsic difference between the people – killing amalek, or someone chayav misah, as opposed to everyone else – then one has a sensitivity, one not. And if you feel bad about the killing, then you’re being ‘more sensitive’ than the Torah – precisely the problem by Shaul.
As opposed to our discussion, where there is no difference between the animals. The question is just WHEN. So if we have two identically blameless animals, and we kill one foe the mitzvah of being happy on Yom-tov, i have a problem seeing a sensitivity towards killing the other (for a useful purpose). Just a svara.