It would be interesting to know what zapper you have ?Is it a zapper or frequency generator?
As previously said the zapper produces a square wave at the fundamental frequency, say 15Hz/2.5KHz etc and then produces harmonics of lesser amplitude/power at multiples of the fundamental. The purpose of this is producing lots of different frequencies that can target many different pathogens. However as the harmonics progress along the spectrum they get weaker and thus less effective.
A frequency generator produces a relatively pure square wave of just one frequency. This is designed to target a specific pathogen whose resonant frequency is in Hulda Clark es list. if you know what type of pathogen/tumor/ parasite you have then this should be a powerful device. However, it is suggested that these are only really effective in the bloodstream and that they have trouble penetrating the organs. That is why when you and your friend hang on to the zapper, the measurement on the scope DMM changes. Your body has an impedance/resistance that will effect the output.In much the same way, some parts of the body will be denser and it will be more difficult for the signal to penetrate it.
If you try and measure the output of a xapper with a multimeter that is measuring the RMS [route mean square] of the signal you will get a different answer than if you used the same multimeter to measure the output of a frequency generator that outputs a pure square wave of one frequency. With the zapper it will be measuring not only the fundamental frequency but the energies from the harmonics. I am surprised you only got 10% error.
it would be much more interesting to look at the scope display. Selct FFT and it should show you a spike at the position of each fundamental and at each harmonic.
Sorry if this is not much help but AC measurement is one complicated subject.....