I would be careful with OxyDeep. As far as I know it contains hydrogen peroxide, and even in a very weak solution, you would be risking color-fading.
My rule of thumb is: If you wouldn't bathe a baby in it, don't use it on your H scarves!
Even with Woolite, I use just a smidgen - far less than the recommended amount.
I think you might be thinking of OxyClean. OxyDeep doesn't have peroxide in it, at least not on the label of the bottle I have. I've used it on dozens of H scarves with no issues.
Someone told me Woolite leaves a residue, so now I use a drop of shampoo or an unscented dishwashing liquid as the soap.