How low does the simulation require the Joules to go to work properly?
About 10J.
Below is the LTspice sim of the circuit which stores 10J in the capacitor:
It is directly powered from the line (be carful when working on it and only plug it to a GFCI socket) so the required isolation to the fence is provided by a dual-output (lost spark) type coil which is isolated from primary to secondary (standard coils are not).
C1 is a low-cost, motor-run film type capacitor whose AC impedance efficiently limits the charging current through the rectifiers to the storage capacitor C2.
C1's value is selected to charge up C2 to the 100V trigger voltage in about a second.
C2 is a 2mF (2,000µF) electrolytic, that stores 10J of energy.
(That's about the maximum without overheating SCR U1)
When C2's voltage reaches 100V (green trace), Zener D4 turns on the transistor to fire the SCR and rapidly discharge the capacitor through the coil's primary to generate the spark (yellow trace).
The SCR dissipates about 2 watts in operation, so may need to be on a small heat-sink.
The diodes shown were the only 3A, 200V diodes I had a model for, but you may want to substitute 3A, 200V Schottky's for lower dissipation.
One caveat is that the circuit has only been simulated, not built, so some tweaking may be necessary to get a real circuit to work as desired.
