Just putting a capacitor on the output of the stun gun will not improve it - it will change the shape of the output wave, and probably will decrease the output voltage, by loading the transformer.
The diodes in a voltage doubler are quite necessary - Let me use an analogy - Imagine it as building a two-storey house - except we are building it a strange way...
Build one storey first (on the ground). Now jack it up into the air, and build the the lower storey underneath it. You need something to hold the top storey up, while you build underneath. This is what the diodes do.
Voltage doublers can be added together to make voltage triplers, quadruplers, and so on.