what kind of shampoo/rinse for dog with cushings?

older pomeranian female with thin skin and a bit of the crusties. needs to be bathed and brushed more, but starting her off with coconut oil and good dog shampoo and conditioner.

shampoo ingredients:
coconut based shampoo, oatmeal, yucca, salicylic acid, papaya extract, tea tree oil, vitamin e, aloe vera, kiwi.

rinse ingredients:
oatmeal, beta-hydroxy salicylic acid, bitamin b5, vitamin E, kava extract, hydrolyzed wheat protein, alpha-hydroxy malic acid, omega 3 and omega 6 fatty acids, vitamin A

is the tea tree oil and the salicylic acid (as well as rubbing coconut oil into her skin which can have a drying effect) going to be too strong for thin skin from cushings? Tweet