GS, you're a right old softy....but I fully understand. Have experienced the exact same dilemma on many occasions.
Horrible to view and contemplate....worse still to do the right thing. I just don't have what it takes to kill things.
There was a guy in my year at school who could always be relied upon to end the suffering of animals found about the place. He used to help us with these dilemmas. He was dead good at breaking necks of suffering birds, or killing roadkill, which hadn't quite died yet. He freed us of our guilt and responsibility. Never seemed to bother him. In he'd march, do the deed like he was undoing a particularly tricky jam jar lid and then triumphantly stomp off. All cool and casual like.
I heard he's doing time now though, for manslaughter.