Your best bet is to put a resistive load on the supply and ac couple to your measuring device. The frequency range for the noise measurement should be specified. Use a spectrum analyzer to see what shape the output noise spectrum takes. You can read the screen when set to voltage scale and use a narrow resolution bandwidth. The manual should tell you the correction factor.
If all you have is a true RMS meter you can put a simple RC low pass filter after the series capacitor and get a crude measurement of the RMS voltage over the bandwidth which is actually 1.57 times wider than the -3 dB frequency of the filter.
[added later] I forgot to be clear and say you divide the RMS meter reading by the square root of the noise bandwidth which is 1.57 times the 3 dB bandwidth.