Properly done, stripping should not really hurt. Dead coat comes out easily. Some parts of a dog ARE more tender than others, and one should go slow there (just a few hairs at a time) so as not to cause undue discomfort.
Stripping is generally considered to be the very best thing for skin health and coat health. Opinions vary though, as to how inappropriate clipping is on a pet, so you're probably not going to get a definitive answer. Some breeders will die before taking a clipper to a Cairn coat. Some experienced folk report good experiences with clipping and use it on their old ones, where coat quality is no longer an issue. Others feel clipping leads directly and inexorably to poor skin health, odor, and soft coats.
One reason the Coat King is so popular is that while it does cut some coat, it also pulls some coat. For the companion Cairn this feels like a reasonable compromise to many as it is fast and relatively easy, but keeps a certain amount of healthy coat coming in.
If I were paying someone to do my dogs, and the cost was not outrageous, I'd go for the stripped coat every time. I love a nice harsh coat with just a slight aroma of garden dirt

We use a Coat King on our older boy and girl and hand-strip their heads and tail occasionally, along with any wisps along their outline.
p.s. Please don't double post.