I have never hunted squirrel with dogs, although my dad always had coon dogs and rabbit dogs. Started following my dad through the woods and listening to the dogs when I was 6. I missed several days of school through out the years because hunting trips. He had one dog that if there was a skunk anywhere close, this dang dog would kill it and bring it back to us. Then there was also several bouts with poison oak.
The thing is that I was tout not to take chance of just wounding an animal and to not kill something that I could not retrieve. And never kill to just to be killing. If you don't plan to eat it, then don't kill it. Of course there were not any yotes around back then.
My point is Why take a chance. There is no way that you don't know for sure if you kill one in a nest. Not unless you climb up there and check the nest.