In the interest of fairness, the answer to your question is; any experienced electrolysist could (and should know how to) remove skin tags and moles. The problem is, with the harassment of various and sundry Hegemonic Organizations, from the AMA, on down, it would invite harassment and costly legal entanglements for one to advertise this service, although accomplishing the goal is easy.
In fact, simply performing electrolysis around or in any mole has the possibility to remove it, even though the hair was the only target.
Another example of this, is Mike Bono’s Telangiectasia Removal book and equipment. While people performing this procedure take 5 to 15 minutes from meet the client, to saying goodbye and collecting more than an hour’s worth of electrolysis make a good living doing it, the average electrolysis practitioner won’t do it, even if a client asks, even though everything they need to perform the procedure is already in use for the hair removal process they advertise.
It is sort of like your auto mechanic refusing to cut a metal pipe you brought to your muffler service appointment, for no other reason than it is not attached to your car, and he is afraid of what might happen if he does.
But to understand this, you have to know that the US has many silly turf wars like this. If you punctured your cheek, your general practitioner could attend to the wound,and send you on your way. Puncture your cheek and in the process wound your gums at the same time, and he has to give you a referral to a dentist or oral surgeon, even though the gum wound would require less attention that he has already given the cheek, and the time spent waiting to get in to see the other service provider could cause complications.