Well, I think you indirectly answered my questions, but now I have a couple more.
How often does your bumbling wave change its max and min values? You said you wanted to hold the P-P number for a few minutes. Does this mean the wave doesn't change often?
Dougy's circuit as it stands has no way to discharge the output capacitors. If the peak values of the wave decrease, the circuit won't reflect that fact until the voltmeter impedance discharges the caps, which could take a long time if the caps are big and the voltmeter impedance is high.
You also haven't said if this is a situation where you will be making these measurements on an ongoing basis, maybe for weeks, months or years. If it were a long time, building a special circuit could make the measurements more convenient.
If you want a quick solution and you're only going to do this a short while, just use a suitable DVM. My Fluke 187 (and numerous other hand-held DVMs) has a min-max mode. You just put the meter in that mode, wait a while and you have both the maximum positive voltage and the maximum negative voltage. The sum of the absolute values is the P-P voltage, and the DVM will hold the values as long as you want. Assuming that the wave may change values and you want another reading, reset the meter and do it again.
If your wave only changes its peak voltages very slowly, and you really want a single number and no arithmetic, you could do this with one capacitor: simply pass the wave through a suitably sized capacitor and clamp the output side with a diode so it can't go negative. Then the voltage there will be a positive only wave whose positive peak will be equal to the P-P value (minus the forward drop of the diode, a Shottky maybe), which you could measure with the peak holding capability of a DVM; this way, you only have one reading to note.. You could use an opamp based ideal diode to clamp and avoid the forward drop error. With any of these capacitor holding methods, you need to reset the capacitor voltage(s) to zero before you take another measurement.