A $5 DMM can do the same thing with DC. However there is a galvanic voltage between the electrode metal and skin that varies with pressure. THese devices are rather poor sensors of intended emotional response and will be more affected by motion and pressure. The fingers may have poor sweat glands compared to areas of smooth skin. But then large areas will be more prone to galvanic pressure voltage. ( battery effect on electrodes)
I suppose they use suitable materials and even pressure to stability the readings.
What happens on maximum gain?
If touching the ground on the sensor input box does nothing to change the values, there is not much chance of improvement with a shield. You can try aluminimum foil while touching device input ground or nearby connected gnd.
My fingers resistance can vary from 5M to 50k, if wet, depending on contact area.
A more accurate method uses capacitance so that the DC galvo voltage ( battery effect) is avoided and conductance is a function of dielectric moisture content.