We can, in theory (and not at the large scale required to feed 8 billion humans), kill an animal without any pain. However, this does not make the act of killing morally acceptable. Killing animals, thus depriving them of their right to life, for selfish desires like your appetite, is wrong.
The definition of the word “humane” is:
“Having or showing compassion or benevolence”.
Synonyms include “compassionate”, “kind” and “considerate”. Therefore, “humane” and “shooting animals”, are not compatible.
No truly compassionate person capable of empathy would want to take the lives away from animals for something as trivial as a sandwich filling.