If you have an ohm meter that would have low enough resolution, you could measure the shunt. First measure the leads touching and then measure the shunt and take the difference. My guess is that you will find it nearly zero. Most people don't have low resistance measurement capability.
If you have a constant current source, then you run the curent through the shunt and measure the voltage across the shunt.
What if you don't have a constant current source, then what you do is find a low resistance (and stable) device and load a power supply with this low resistance device in series with the shunt.
What kind of device might you have? An incandecent bulb. Find a low wattage bulb and make a circuit with a power source, the bulb, and the shunt. Don't get shocked - be careful. What you have created is a voltage divider with two resistors. Now you need to measure the total voltage across the two loads and across each of the resistors. The current through the bulb and the shunt is the same. The resistance across the bulb should be much greater than the shunt, so you can estimate the resistance of the bulb and thus calculate the current and knowing the voltage and current through the shunt, you now have it's resistance.
Here is an article with schematics and formulas to calculate this voltage divider:
https://en.wikipedia.org/wiki/Voltage_divider

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