I am a chemical engineer. I also have a masters degree in toxicology. Again, I have a lot of electrical experience by modifying audio components (preampliers, amplifiers CD players, speakers...).
My VOM (Fluke) has a resistor of 115 ohms when used to measure current (set at 2 milliamps), hardly high enough to impact current when measuring my body's resistance. When set at 20 milliamps, the VOM's resistor in series with the current is 15 ohms, again, hardly high enough to impact measuring current. I can try a resistor in series with the zapper current, if I can find one of that value...
I would like to raise a new concern about zappers. If zapping parasites requires current above 1 milliamps, there is some evidence that zapping with currents greater than 1 milliamp has a deleterious impact on cell health, although at current levels below 1 milliamp cell health is improved. I want to be really careful here because the studies that show this deterious affect may not apply to real life situations. The data I have seen were collected in in vivo studies (rat and horse live tissue subjected to microcurrents outside the animal from which the tissue came). In these cases, all the current was channeled through the specific tissue being studied. However, when a whole creature is being subjected to microcurrent, current levels would be lower through most tissues because of the increased number of pathways that the current can travel through. Of course, certain tissues are more conductive than others and they are more likely to see something closer to the full amount of current. Also, it is not certain that human tissue would have a same or similar reaction as animal tissue.
However, health impacts on animals or animal tissues are routinely used as surrogates for estimating impacts on humans. Because of this I would be cautious about using a zapper - particularly if higher currents are being passed through the body. Certainly if someone knows that they have a parasite, I would not hesitate trying a zapper. However, if I did not think that I had a parasite, I would not zap "just in case" or "for the fun of it." Some people may even strap zapper cables to their ankles or wrists and zap all night while sleeping. If the zapper current is low, then I probably would not have any concern. But higher power zappers could be a concern.