I wish I had a dollar for every time this has come up on gun boards. But it's an honest question. It gets a lot of interest.
I saw the movie in theatres and several times since. I think I have the DVD. I even have a letter from Boothroyd on the movie stationery! Yes, really. I was a fan of James Bond from my early teens and read all the books and eagerly awaited the first film.
I corresponded with the REAL Geoffrey Boothroyd, who looked nothing like the "Maj. Boothroyd" of the film. Nor did he advocate the PPK. That was Fleming's idea, after reading an article on several enemy pistols from WWII compared to the US .45 auto. He liked the idea that the gun was easily concealable and that the .32 auto (7.65mm) held more shots than would a revolver. (But Bond did use a snub Colt .38 as well as his famed Beretta .25 in, "Casino Royale." Fleming described it as having a "sawn barrel." He may have just not realized that the factory supplied snubs as such, or may have seen a cut-down Police Positive Special.)
Mark you, we don't know the model of the "long-barreled .45 Colt" that Bond had under the dash of his Bentley. I think it was probably a .45 auto, but it could easily have been a New Service with a 5.5-inch barrel, as the author owned one and appeared with it in a major feature on him and his books in, "Life" about 1960-62. Several of his other guns were also shown, inc. a Ruger MK I .22 target auto. I think this was the long-barreled .22 auto that a girl had in a short story. He simply equipped her with a gun that he owned and knew about and liked. Just my guess, as he didn't state the brand.
The Colt Official Police .38 with four-inch barrel that he held on the back cover author photo on many paperback editions was given to him during WWII by Maj. Gen. Wm. Donovan, head of the OSS. Fleming was then an assistant to Britain's chief of naval intelligence. He carried a Browning Baby .25 in that role, but probably had access to other guns, if needed.
Bear in mind that as a spy, he HAD to be confident that his gun could be effectively concealed. That life was not a movie!
Bear in mind that he did own at least 4-5 handguns, and he did this in the repressive atmosphere of Great Britain. Even in the 1960's, he had to endure a lot of red tape to have those guns licensed to him. He must have cared enough to do that. But he was not a gun expert and indeed suggested in one book that having an "excessive" interest in guns was abnormal.
Geoffrey Boothroyd really was a gun expert, and his, "The Handgun" is easily the best study of its kind and should be in the library of every gun enthusiast. It covers the subject from earliest days to about 1970, when it was published. Find it. Buy it. Or be ignorant of much that you should know.
Now, as for the movie: The gun that Connery is holding is a Browning/FN M-1910, not a Walther at all. And, OP, the name is "Walther", not "Walter." But the movie Maj. Boothroyd did seem to say, "Walter." His accent? An ignorant error in the script? ??
Obviously, the .45 auto in the chemist's hand is not a "Smith & Wesson" and it held more than six shots. If they had trouble finding a silenced revolver, the script could have easily been altered to reflect that he had a Colt .45 auto. They didn't care, I guess, and thought that audiences would neither care or know.
However, there WAS a Walther PP subbing for a PPK in some scenes. I don't know why. Maybe something to do with prop availability in gun-strict Britain and Jamaica, although that island was then still British territory, a Crown colony.
This is a good time to note that Jack Lord did not look like Felix Leiter and Lord was also an outspoken advocate of gun control. The Leiter of the books was "a straw-haired Texan", a former Marine officer. Leiter was actually played by a black man in one film! The studio has little respect for the details of the books, and I've seen conjecture that this is going to get much worse, in the name of Political Correctness. Can't say more here. But I hope to gosh that it isn't true.
"Dr. No" was the first Bond film and I think its vast success took the producers by surprise and made them financially and made a star of Connery. Their budget got a lot larger and that led to them having whatever guns they wanted, presumably. But, "Dr. No" is the movie closest to the book. "From Russia, With Love", was also very close. They started to lose it by, "Thunderball" and it just got worse. I won't even go to a current Bond film. The first with Daniel Craig was awful, and not just because I don't like Craig for the role. Bernard Lee was a good choice to play M, but he died.
The book Thunderball was better portrayed on film in, "Never Say Never Again", with Connery returning as Bond, but NOT in a production by the usual producers, Broccoli and Saltzman. I think it was better for that.
Anyway, you now know which guns were really in that scene. Maybe the FN was used because the silencer wouldn't fit a Walther. We'll probably never know.
Oh: the tarantula in, "Dr. No" was filling in for a centipede, probably because a real centipede was too dangerous. But I love the scene in the book when 007 woke and realized that the centipede was crawling on him. Fleming knew how to write a tense scene! He was also a real SCUBA diver and often spearfished for his lunch off the beach near his home in Jamaica, where he wrote the books. A famous magazine that once excerpted his novels showed the interior of his home, inc. his bed and the desk and typewriter where he wrote, and the adjacent beach.
Some complain that Ian Fleming didn't know a lot about guns and that's true. However, very few authors do. He owned more handguns than any other author I can think of, save perhaps for Donald Hamilton, who wrote the Matt Helm series and who was also an outdoor writer. John Sandford, who writes the Prey series, is a gun owner, although seemingly a liberal and a former newsman. But he only occasionally goes into detail. Wilbur Smith hunts and is a big game fisherman as well. But his gun stuff is sometimes dead-on and sometimes off a little. He can't own handguns in modern Britain, but may have some at his South African residence. Jack Higgins may own guns, as he lives in the Channel Islands, not affected by the terrible 1997 British law. But he errs in describing the effectiveness of .25 HP ammo and never says where the Secret Service spinoff for which his heroes work got those Colt .25's or how old they are. His other pistols are mostly mentioned by just brand and you have to guess the model in most cases. The Walther PPK and the Browning Hi-Power are exceptions. But, "Ceska" can mean a CZ-50 .32 or a CZ-75 9mm!
On balance, Fleming wasn't perfect, but his guns were as well or better chosen as most in popular fiction. He was wise to seek Boothroyd's counsel, but sometimes rejected it. That's why he messed up and had Bond use a Berns-Martin holster for the PPK. Boothroyd suggested the holster, but for a snub S&W .38!