How to measure capacitor maximum voltage rating
Measuring the transient, you can find only capacitance of the capacitor.

I'm afraid that you can measure only what was the breakdown voltage of the capacitor, if you connect it in series with a current limiting resistor and the microammeter to the regulated voltage source.

When you increase the voltage above the breakdown voltage. The current will increase. Depending on the type of the capacitor it may lead to its destruction (and I wouldn't dare to use this capacitor later on).

Please note, that so found breakdown voltage may vary significantly for different capacitors from the same batch. So the safe operating voltage for the rest of capacitors from the same batch should be assumed to be a few times lower (I don't know the exact number) than the breakdown voltage measured above.