His wife found him dead on a private path near their home.
Investigators told The Henderson Daily that three people were having target practice near the area at the time.
It's believed a stray bullet may have struck the 85-year-old.
Officials interviewed the three individuals -who were not named- and officials said they did not suspect foul play, but the investigation is ongoing.
Satterwhite was a veteran of the US Navy and served during World War II.
His funeral is scheduled for Tuesday.