Seems like a shame to put up a bird house to attract birds for your viewing pleasure or bug control. Then shoot birds that aren’t on your bird watching list. Try and removing there nest first, it may take a couple of attempts but they will move on if disturbed enough. After all sparrows eat unwanted insects as well as martins.
A former neighbor had a Martin sub-division must have been fifty holes in his super size bird house told me that sparrows and martins co-exist well with each other. I never noticed much conflict with my own observation. I spent many hours watching them form the deck on the back of the house.
The Busy Bee teaches two lessons: One is not to be idle and the other is not to get stung.