As with most research projects, you 'know' the information has to be there given Churchill's record in South Africa and his home at Blenheim. However unearthing reliable, confirmable data is proving perplexing. Other than the reference to the missed stag(s) shots, I have found a picture of him on a boar hunt in France before WW1. I have found 'comments' that he was a 'poor shot' but nothing to confirm or dispute that. His preparation to 'die fighting' if the Germans invaded England in WWII incldued practice with a Thompson SMG, and a Webley MK6 in .455. My next step is to contact the auction houses in the UK and determine if any WSC shotguns or other firearms have ever come to the floor. I had hope that perhaps he had purchased a Churchill shotgun from his very, very, very distant relatives, the gunmaking Churchill's but no records of such.
Thanks very much to all who have responded.