If you're choosing the voltage, then you won't get to choose the current. This is because the resistance is already chosen for you, as it is a physical property of your electrochemical cell. Therefore, two of three variables are known in Ohm's Law, which means the third, in this case current, is fixed by the other two, voltage and resistance. For example, using your DC power supply set to constant voltage mode, slowly turn up the voltage from zero. Now watch the current reading as your continue to increase the voltage. At some voltage, the current will spike, as an electrochemical reaction is initiated. In your case, this will be water splitting, evident from gas generation at the electrodes.
The resistance of your electrochemical cell will be dependent upon a variety of factors. However, you don't need to theoretically determine this. The DC power supply is providing all the data you need to determine the cell's resistance! It outputs V and I, so all you need to do is use Ohm's Law to get the resistance (R=V/I). Now you can use this resistance value to calculate the current at different voltages, say 2.5 V. Note that the cell's resistance is dependent on factors like electrode spacing, temperature, and water composition. Hence, the resistance value you derive will only be valid under those conditions.