Connect the cap to a DC source, limmited in current. For instance 100V through a potentiometer with a currnt limmiting resistor from wiper to cap. Connect your LCR meter to the cap via two large HV MKT caps ( like 4.7 uF or so)
The value you measure will be 1 / ( 1/4u7 + 1/4u7 + 1/Cx ) but the actual value is not important. This way you can see the capacitance change. And then you know upto which voltage they are usable. They drop in capacitance before they brek down.
If they do not decrease they will breakdown and You know the voltage. Mount the testfixture in a box as protection for your eyes and kin.
But your oscillator idea is nice too. The frequency tels you the capacitance. You can test voltage and if frequency goes up and you note frequency you lo know the capacitance, with some luck the oscillator stops befor the cap explodes. I ould use a Wunderhorn oscillator, this uses two transistors, tubes, or fets and it oscillates from a MHz upto some GHz. Make a switch and some inductors for a broad range. Add a microprocessor ( and maybe a FV converter and to meaure frequency. The uProcessor can calculate the capacitance and also meaure leakage current and voltage if you want.
Use a servo to control the potentiometer and you even can sweep voltage.
The output of the potentiometer to the X of a scope, a voltge proportional to C from the microprocessor to the Y and you can ake graphs.
Nice, good idea, i have the sme problem, thausants of unknow caps. Most pF ceramic. This test eill give a clue sbout the type and rathing.
i think I'm gonna do that one day. But a bit different. I am not a uProcessor guy but I can sweep the voltsge analoeg using my fingers to turn the pot and use my HP 135 X,Y writer for the plots. The X input to the wiper, the Y input to a IV converter i once build to meaure fF ( but it can do nF or uF as easy), choosing the right gain and frequency that gives a voltage reading in direct in capacitance. I measured fF that way. But the value is not important, it is about the change invalue.