If the current (or power) is small enough or for AC single: the frequency is high enough.

Our heart beat is also driven by small electric signal.
It could be dangurous if the current happen to influence your heart beat (stop) .
So even small current (1-10mA) could be dangurous.

It is much safer if the current is less than nA or even smaller.

Actually, if the voltage is too larger, it will break down even across air. (e.g. 20kV/cm at 1atm)
So you would not be able to find a constant voltage 10[sup]10[/sup]V wire.