Here's a link to the story of the person who cut her dog using a Coat King...
http://www.midlandctc.co.uk/news/coatkinggroomerwarning.htmIt was being used on the throat, which as Mike says has folds of skin that are more easily caught between the blades. Also this dog was a Cairn Terrier so the Coat King used would have been a 6 or 8 blade one. The blades are much wider apart than on the 26 one you would use on a Cocker. It isn't recommended for use on the throat.
This site shows pics of all the different bladed Coat Kings, you can see how much wider apart the blades are on one for a Terrier...
http://www.denbar-uk-ltd.co.uk/acatalog/De...t_King_262.htmlIn areas where the skin doesn't lie so flat (like the thighs) , if you spread the skin out with one hand whilst dragging the Coat King through with the other, then you won't have any problems.
I wouldn't use it on the head really, either. If you are using thinning scissors to trim the head, brush the topknot forwards so it stands on end, then cut from the back of the head in the direction towards the nose, brushing out between cuts. You won't get as sleek a finish as you would by handstripping but still neat and tidy enough for a pet Cocker. I've stopped handstripping Jimmy's head as I think he looks better with a little bit left on top, I just use the thinners now.