This is not my line of work, but have been down this road.
We live in a 100-year-old house, when we moved in the refrigerator had a similar problem.
I upgraded to 3 wire receptacles and added a ground wire to the back of the fridge GROUND SCREW, did the trick.
The main tool I used was a Greenlee GT16 noncontact voltage tester. *Note the model goes to FIVE VOLTS, many others only read near 110 volts.
https://www.greenlee.com/products/ADJUSTABLE-VOLTAGE-DETECTOR.html
I check the voltage tester before EVERY USE by rubbing it past my sleeve or the carpet to see it light up.
Guessing that somewhere there is a ground fault, I had the fridge and an old desk fan.Upgrading to 3 prong receptacles that were properly grounded was the answer.
I did the work slowly over some time.Checked the work with an inexpensive tester:
https://www.homedepot.com/p/Power-Gear-3-Wire-Receptacle-Tester-50542/206212329?cm_mmc=Shopping%7CG%7CBase%7CD27E%7C27-11_TOOLS_%26_ACCESSORIES%7CNA%7CPLA%7c71700000034238984%7c58700003943782712%7c92700031954542185&gclid=CjwKCAjww6XXBRByEiwAM-ZUIABo9CR69SvEPVdvwmER08TVbsTrEzktIHKid7dpVaUIArjpRIXm6xoCkrgQAvD_BwE&dclid=CMqLiPqr59oCFUOUaQodcSMI-g
My retired cousin did her entire old house while her husband was working out of town, slow but sure.
One reason some people feel it is called skin resistance some have dry skin and higher resistance to the flow of electricity.
Try grounding the faucet from underneath the sink to a clean metal pipe. sand the pipes to shine them with sandpaper,use ground clamps and copper wire.
Clamps like this one: https://www.grainger.com/product/2DDE7?cm_mmc=PPC:+Google+PLA&s_kwcid=AL!2966!3!166591489617!!!g!137372519842!&ef_id=WtdOrwAAAH85oxA0:20180502153458:s
I just returned from a business trip and have a number of questions, but too tired to ask them. One, however, I am not clear on your suggestion to ground the faucet from underneath the sink. The faucet fills the bathtub, comes out of a tiled wall and the tub is set in a tiled concrete basement floor. Of course a refrigerator is an electrical appliance; a bathtub is not. More after I have a chance to go over all this with my electrically inclined friend. At any rate, thanks for suggestions, both of you.