Here’s a compact device that will take a 9V input (from a small battery) and output high voltage close to 10KV that can be used as a gas igniter or as a stun gun.
It uses a small Armstrong feedback oscillator driving a small ferrite core with a high voltage secondary (from TV), and a multiplier. The schematics for the oscillator are available here.
This battery powered high voltage inverter is easy to build. The flyback output is close to 5KV. The multiplier is a 4 stages Villard cascade.