With even smaller capacity.
There's more physical volume in the casing and air space in that pack than there could possibly be by chemistry. Stuff like that should go into an engineering monstrosities 101 class of what not to do when designing efficient systems.
for high voltage circuits, you can use the board inside insect killer that uses a 1.5v cell and generates high voltage. i have seen some like that like a tennis racket with mess of wire to charge it, operated by a single cell.
What about the guts from a camera flash unit. Wayyyyy back when the 126 series cameras first hit the market, they used a "flash cube" that did exactly what you want. Multiple stages of voltage doubles with steel wool inside the flash cube. Ran from one small battery, I disremember what size, but the camera would fit in my trousers pocket.
If I recall correctly, the "disposable" cameras that sell for about a buck do have a flash.