I'd try not to put myself in that position but if faced with it....
1.Wouldn't shoot.
2.I'd recover the deer

My Dad shot a buck once and it died on anothers property.It was close to the fence and he didn't ask for permission.Well hewas caught in the act.The owner told him he was taking the deer,soDad volunteered to gut and help drag it out.The guy declined his services and they parted ways.As far as I know there were no hard feelings on either end.The moral of the story is if your going to dance you have to pay the band.