Preamble: This is meant to be a technical analysis. This is not a post about gun control. Comments about Japanese and American gun control (or any other nation) will not pass moderation.
This is probably the best photo of the assassination gun that I have seen:
Witness reports stated that there were large puffs of white smoke. Between that and the photo, this is my guess:
What we are looking at is a completely homemade gun. The base of the barrels appear to be capped off with threaded caps. Wires are going into the caps. Under the barrel are what appear to be either batteries or capacitors. In short, that is a two-shot hand-cannon; a marriage of 13th Century weapons technology and 20/21st Century electronics.
The ignition system is likely some sort of electric lashup. The simplest way to electrically ignite the charge would be by using model rocket engine igniters. The battery/capacity lashup was likely designed to send a fair amount of current to the igniter, in order to achieve near-instant ignition. Another method might be to use light-bulb bases (remove the glass bulb and leave the filament intact).
The powder charge was almost certainly black powder. Black powder can be obtained by several methods. It is fairly easy to make, given that gunpowder was first manufactured well over a thousand years ago. It can also be obtained by buying firecrackers, opening them up and pouring out the powder. I cannot overstate how dangerous this is.
There are basicly two grades of black powder: A and G. A grade is used in fireworks, G grade is used in guns. Guns use variants of Fg black powder. The "F" stands for fineness, graded by the mesh size of the sieve that the powder will pass. The more Fs there are in the powder designation, the finer the powder and the more quickly the grains ignite. FFg powder is commonly used in large-caliber rifles and handguns. FFFg is used in smaller-caliber rifles and handguns. FFFFg is used to prime the pan on flintlocks and wheellocks. My suspicion is that, historically, the soldiers just used the same powder for priming, as they'd bite open the paper cartriddge, sprinkle some powder in the pan, close the pan and then load the gun.
Black powder, unlike smokeless powder, is an explosive. A properly loaded blck powder firearm has no airspace betetween the propellant and the projectile(s). When the powder is ignited, the pressure builds up and pushes the projectile down the bore. But if there is a gap between the projectile and the powder, the pressure builds up far more rapidly because there is is somewhere for the pressure to go. In that event, the gun might blow up.
Firecracker powder is very fine, the pressure spike from a charge of that might be pretty dangerous. The reporting seems to imply that the assassin did some testing, so he may have been aware of this.
On another note, take a look at the belt holster of the bodyguard:
That appears to be a revolver holster for a gun that's not very large. My guess would be something along the lines of a S&W Model 60 with a 3" barrel.