I would probably chose a Colt New Service AND a Winchester M1892 chambered in 44-40.
In fact, I did arm the character Finn with a M-92 and a 6.5mm Mannlicher-Schoenauer to replace the crossbow that she had on the show, but her handgun is a M&P .38 with five-inch barrel. In the stories, Finn got these from other expeditions that had perished like that in the TV episode, "Suspicion."
In later fics, set off of that strange Plateau, she often uses a .275 Rigby for her light rifle and a H&H .375 or a .450/.400 for elephant, occasionally Cape buffalo.
I based the Winchester .44 and the Mannlicher on what I knew actual expeditions often took in those days, and on Siemel's comments on how popular the M-92 was. Rossi still makes a copy of it there. We know the Challenger Expedition found tha remote plateau with the dinosaurs, etc. in Brazil because the canoes went upriver from Manaus in the two-part pilot show. And I thought those guns would go well with Finn, a cute blonde.
Most of the guns carried by the others were typical of those favored by the British gentry, although I had Ned Malone, a famous author by the later fics, use a Griffin & Howe .30/06 on a Springfield action and a .270 Winchester M-54. He was American. Also, in a safari story, Finn's secretary, Susan Wilson, had a 20 gauge Remington pump shotgun, with which she killed a hyena in her tent, and shot some chimpanzees that had taken to attacking people. She found slugs very effective on them, and Marguerite (by then Lady Roxton, the Countess of Avebury) dropped one chimp with 12 gauge Purdey. She was loaded with birdshot because the stony hill they were on looked, "snaky" to her. The chimp was so close that the shot didn't have time to sepaate much and hit the ape in a virtually solid mass.
Surplus guns being cheap wasn't a factor for these people. They were discerning and well-to-do, Finn having married Challenger in the stories after his wife died. She became an author of adventure books and a pioneer wildlife photographer and a famous huntress/adventurer. Her secretary, Susan, had been a bank clerk, and bought har own revolver, a .303 sporter from BSA, and the Remington shotgun, but Lord Roxton and the Challengers bought her a .375 H&H, Lady Roxton having taken a liking to young Susan. (Susan heroine worships Finn, who is the virtual little sister and primary hunting partner of Lord John Roxton in my stories.)
Someone mentioned that many Latin Amercan countries ban miitary calibers. I thought of that, but don't know when it began, so ignored it. I think Brazil had pretty lax gun laws until at least the 1950's. None of my fics is dated beyond 1944, and all the others are from 1922-1929.
I can well believe that Baker, as one member posted above, had Colt's revolvers. They were very popular among British adventurers in those days.
I guess that if I write another story in which different guns appear, Second Model .44 Special or .45 Colt guns may be the answer. I had one safari fic no longer on the Net where the District Commissiner in Kenya used his S&W .455 from WW I and a white hunter had a Colt New Service .45 Colt. A gentleman farmer wore a Webley-Wilkinson, Model of 1911.
These fics are fun to write, and if the urge is overpowering, I may write another. But the show hasn't been on in several years, and the fan base is waning. Still, it's fun to fantasize about the guns and other gear. (I have them use Zeiss binoculars, as many famous expeditions really did.)