I am afraid I have no knowledge on censorship for this film. What I can tell you is that the scene you describe was that way in '62, and was not the result of any censor cut. The style of editing adopted in this film started by director Terence Young and editor Peter Hunt was daring for it's time. If an actor or actress doesn't quite get the action right or stumbles, the editor can remove the offending frames. The skip in the picture is covered up, in this case, by the sound effect of a gun shot. Later, there is a scene in Strangways home when Bond is examining a photograph and he asked the police officer who is the man with Strangways. Apparently the actor walking in was late on his cue, so editor Hunt removed a few frames to speed up his entry. If you watch Connery's face right after the dialog you can see the cut.
I believe these are called jump cuts, to speed up the action. There is another method called step printing where every other frame, or 2 or 3, are removed to achieve a certain dramatic effect in a fight etc. Peter Hunt utilised and perfected this editing style throughout the Bonds he was involved with (up to "OHMSS").