I don't know much about switching foods with a pup that gets hypo, but I do have experience with scratching.
There were two causes of scratching for us. One cause may not require you to change foods.
The first problem could be a yeast infection or fungus infection. (If it's in her ears and on her nose it's called leather ear, I believe.) Anyway it seems that yorkies are prone to fungal type infections. A solution of 1% lotrimin (athlete's foot medicine) or an antifungal from your vet may clear it up.
Daisy's fungal infection started with a rash between her shoulder blades.....which sounds like your problem.....
Also, Daisy scratches when she eats food that has corn, wheat or dyes in it. I don't know if all of these cause the scratching or just one - it seems that a food that has one of these ingredients has all of them.
Good Luck - that scratching about drove us all crazy!!!