Kill general and cover killbots as infected by chineese,Moscov,something.Maybe bad polish antisemites? according to Izrael,we are responsible for Holocaust.Why not killbots,too?
Weird pivot politically ngl lie, but sure. Maybe?
The problem then is that Skynet can't really do that. It needs those nuclear launches to decapitate the command and control network of the world. It was inside every networked civilian computer, and every networked American computer; so presumably the initial few hours before it launched nukes it was making sure that it had thoroughly disabled any defence, early warning radars, etc through malware. Then it launched.
So what probably happened was that Skynet waited for all the command staff to get into their bunkers, or on planes heading toward secure locations; or even just took the time to shut down infrastructure it might need for re-activation post bombing; and then fired off the apocalypse load. Without that load, lots of people are still going to die because hey, all the power everywhere just got cut. But I don't really see how it can thoroughly decimate the US's upper command like in the OTL. Skynet is smart, but it's working with maybe ten or so weapons plants, a few dozen unnamed drones. The response by the government will be slow because they won't be able to contact each other; but eventually some NG units, or even a full scale military response is going to trickle down and they'll blow up Skynets manufacturing centres.
Killing Skynet completely though? Nah, we're fucked. A skynet clone/copy/instance was running on every computer that ever connected to the internet. We're heading straight back into the 1950's technology wise. Anything more networked than a punch card machine now harbors a pissed off genocidal war AI.
EDIT: It's still going to really, really, really fucking suck for the developed world though. If it can't get us through the nukes, and it realises that there's no ending where it wins; it might be self aware enough for that oh so human emotion of 'Spite'. It could cause every nuclear plant to melt down, destroy our economy, overload substations, cause untold deaths in cities through power overload fires, hospitals turning off, pipelines overpressurising and blowing up. Etc, Etc, etc. Not a fun time.