oh dear ...
that circuit has a lot of problems ... let's see ...
If the capacitor is empty (probably after each sparc but certainly on power up) you might have a very large load current. The current depends of the equivalent series resistor (ESR) of the cap, but could easily go into the 10th-100th of amps. Possibly too much for the rectifier and transformer.
If the rectifier fails for any reason and AC is delivered to the cap, I don't want to be in that room... Especially not with that cap size!
The fuse is absolutely useless if it only blows on a dead short (that is exactly what you are after for the effect!?). Either it will blow all the time (good for safety, bad for the effect) or it will never blow at all (bad for safety).
The momentary switch is useless too, because it will instantly melt its contacts together. No safety at all!
The "load resistor" will die, because its rating of 10W is too low. After rectification you will have about 17V (1.414 * 12V) -> Nearly 30W power loss in the Resistor -> Resistor dies ...
Brainstorming of dangers:
Flying molten metal, UV-rays from the arcs, noise, fire-hazard, explosion hazard (cap), chemical hazards if that huge cap explodes/vents/melts, EMI interference with other devices, electric shock hazard if the transformer fails (because it has no fuse to protect it...)
If the fence is grounded, any contact of your "rod" to any other grounded part might overload the ground-system of your house (that sometimes happens with electric arc welding ...)
Ok, my opinion: Just don't do it! It's a really bad idea!
Play safe,
Pete