It doesn't annoy me, Paddyann Your garden, you do as you wish. A shotgun is a bit of an overkill with a small animal like a grey squirrel, anyway.
However, if the greys should develop a "bit of a sniffle" perhaps it is would be worth considering that a sniffle in a grey could become a nasty and fatal infection in any reds that are still in the area. "Quantitative evidence from the red squirrel stronghold in Formby, Lancashire where greys are controlled within the stronghold indicates that reds can become infected and that this leads to an epidemic that results in approximately 80% mortality" Livingwithpoxreport.pdf There are some really horrible photographs on the net of red squirrels with this disease. Perhaps if you knew it was in the area, the shotgun would seem the lesser evil (when the GC were not around!)