I think your argument is flawed since many animals arent killed in a humane way anyway. If you are that worried about the way the animal was killed wouldnt you just avoid eating meat? or wouldnt you make sure that you only ate free range, non factory farmed meat? In which case youd have to ask about the way the animal was killed every time you were going to eat meat.
Also, if killed properly (halal wise), the animals are meant to feel very little pain and the animal is not meant to be aware of the fact that it's going to be killed (to avoid it becoming frightened)
Another thing which doesnt make sense to me, is that you're bothered about the animal being killed in God's name. I dont understand why you would be bothered if you dont believe in him?
I dont know if I'd be offended but, no, I wouldnt cook non halal meat for you. Even if I wast eating it, I still believe it wouldve been killed the wrong way, so it doesnt change the fact that I believe I shouldnt support the killing of animals in a non halal way. If I was cooking Id probably not be cooking meat anyway, because I prefer not to eat meat.
Which brings me on to another point. I was pescetarian for a few years because I didnt agree with the way animals were killed. (I eat meat now, mainly for health reasons (but I plan to go back to not eating meat soon.)) Halal or not. The reason being, unless you actually see the animal being killed, or trust the person doing the slaughter, you dont know for certain, that the animal is being killed the way you think it is being killed. So although muslims still buy halal meat, it's on a trust basis but, Im pretty sure that a lot of the meat marked 'halal' isnt actually halal. As it's been found recently, there is pork in 'halal' sausages. I'm sure if you went to halal slaughter houses youd find they were not killing and looking after the animals in the correct, Islamic way.
So, I think if you are bothered about the way animals are killed, it's just best to avoid eating meat.
Hope this made sense. Excuse any (typo) mistakes.