There is no current without voltage, what you're saying makes no sense.
Current is voltage over resistance, you get as much current as you have voltage, unless there's an artificial effect limiting voltage, like a voltage regulator or zener diode or just fet.
When you say 'it's the current', that electric fense has x volts before you touch it, and the fact that it doesn't kill you means either the voltage is too low to produce a decent current in your body, or, there's a voltage regulator/limiter that means when you touch it the voltage drops to some lower level, which I could calculate using the nominal resistance of the human body and the voltage of the fence.
In a way, the output impedance of whatever is driving the fence determines how much the voltage drops under load.
I'm speaking about the voltage needed to get the deadly current across the critical areas of your body BTW, which can be handled as a kirchoff circuit I'm sure.
Arcing causes more fires, because over current caused all the fires until we tightened standards and dual-mode circuit breakers.
Now fires are caused by loose connections arcing, and damaged wires arcing to flammable material.
Breakers are specifically designed for a sustained current, but arcing is dangerous because it tends to cascade, light arcing damages contacts, leading to more arcing in a cycle.
The real danger of arcing is that it can happen outside of view, and start fires that aren't caught till everything burns down.