Hi there.
I have a hornets nest close to one of my apiaries - yes, there are usually one or two hornets about picking out the odd bee.
But as a poster be4 in the thread posted - peanuts - surely not a reason to go killing them off. Birds will catch more a day - you going to sit next to your hives shooting birds next?
Plus - I hope you know where your bullets/pellets go to if you miss - or even if you don't. Not everybody reading this thread may be able to add 2 and 2 but have a gun of some kind.
Of course the hornets will pick out whatever they can get - and sure they will also take a guard bee if the opportunity arises but that is life.
They usually go for bees that are hanging about or when they come out for orientation flight (also only a limited time of the day).
If they strip a colony then there was something wrong in the first place. But before that happens the wasps will do it.
So apart from the thrill of shooting them and the irrational fear of being attacked by them, there is no reason to go killing hornets IMHO.
Greets
Phil