Well I don't know what happens if you tell kenny/katja to kill duck and I don't wanna know until I try it on different saves but as for deciding to kill him yourself I see it this way:
They did want to say their goodbye's right ? Well maybe when katja and kenny were in the forest, katja told kenny that she needed a moment alone with duck, or maybe she told kenny that she'll do it. As soon as kenny gives her the gun, she shoots herself
What do you think ?