I groom some myself and sometimes I take her to the groomers but sit with her as she clips and shaves Lola.  Recently I had the groomer shave down her underbelly really close.  While I saw NO burns or nicks and everything felt as smooth as butter it drove Lola nuts so much so that she licked under her chest non stop till she wound up with raw red spots.  I kept rubbing a little Vaseline over the area to sooth it and put her in an over the head cotton stretch dress that had elastic around the lower tummy so she could not get to the spot that bothered her.  Do not use Noxema, it has menthol in it and to me I remember that stinging when I used it years ago.  Anytime you put something topical on a dog you need to either put them in a head cone or cover the area with something like a shirt or a onesie, if you don't they will like all the crème off.      
My advice is not to shave your dog so short that if feels like a crew cut to them, instead leave a little bit of hair, this will protect the dog against the sun, yorkies are meant to have hair, so while I understand you not wanting long hair, you don't have to shave them down to achieve an easy to manage hairstyle for you  and a comfortable length for them to handle the hot weather and sun in the summer        |