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.