There have been a few movies, mostly set in Africa, that were centered around hunting or capturing wild animals, in which guns appeared in a normal way, not that going on safari is particularly normal. Easily the best is John Wayne's Hatari from the early 1960s. That one was about people capturing animals for zoos but there's some shooting, though not at animals. Interesting scene of shooting at bottles, just to see how well someone could shoot. They don't make movies like that anymore. Come to think of it, don't remember any like that earlier, either.
The first Tarzan movie with Weismueller was based on a safari and there is also some shooting but guns don't otherwise enter into the storyline, as I recall. Tarzan, of course, never uses a gun, his knife being sufficient, and neither did Weismueller's reincarnation as Jungle Jim, even though his enemies (it is enemies that make life interesting) always had guns, if only very ordinary guns. A couple of them even had big gunfights and in one he promised to teach the female lead how to shoot.