Assuming they will come to a cottontail in distress call....mouth blown or electric?
Either will work, I would personally use hand blown. Are you going to be hunting them specifically, or just shoot them if you see them deer hunting?
Could I use a turkey load in a 12ga and try to get them within 40yds?
Don't see why it wouldn't
Or would a 22lr be enough for a fox?
Probably, but if your not going to mount them, and you are just trying to get rid of them, shoot em with the .270
I figure hunt the wind like you would with a deer
You are correct