Measuring Leakage Current in a Splice
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Test setup.

You don't run current through the conductor. You just apply voltage to one end of it relative to the other electrode in the tank it. If the splice insulation is good no current will flow. 

Figure 1 shows a second electrode. If a metal tank is used it could act as the electrode.

Current limiting

I recommend that some form of current limit be added to the circuit. Without it you risk damaging the ammeter in the event of a bad insulation breakdown or accidental short-circuit. I presume you are interested in leakage currents in micro-amps which would equate to a leakage resistance given by \$R = \frac {V}{I} = \frac {50}{50\mu} = 1~M\Omega \$ for a 50 uA leak. Setting R1 to 10k would limit the short-circuit current to 5 mA and give a 1% error on a 1M leakage.