I wouldn't even spend time thinking about it for $10,000, as it wouldn't change my life in the least. For some people it could though, so I don't judge them. They could be homeless and on the verge of death, or need to pay for a loved one's medical treatment.
If it were $10 million, then I would begin to think about it. I could rationalize it by saying that there are millions of random deaths all the time. People dying in accidents, infections and disease, weather, war, etc. People die randomly all the time. And there's a good chance that the random person being killed won't be missed by society. Maybe that random person was a bad person such as a serial killer, pedophile, rapist, etc. Maybe they are very old and dying anyway, or suicidal and don't want to live anyway. Maybe that person would be kill someone, and you can prevent somone from being killed.
The odds of you killing anyone in your close circle is essentially zero. Tenmillion dollars would allow me to invest the money and live comfortably, and over the many years I could share my wealth wih many people to do good.
If there was a button that I could press to transfer 10 million dollars into my bank account, and somewhere someone in the world would randomly die, it would really make me think.
$100 millon and I'm sure I would eventually press it.