I'm having my third Fraxel dual treatment, can I cleanse my face with just cold pressed hemp oil?

Will it keep my skin clean still or should I use a different cleanser? I know right after Fraxel is a time for healing and I just don't want to mess up my results. Hemp oil is what I have been using as face wash and lotion since Cerave started causing dermatitis after years of use. It removes my makeup and doesn't seem to cause redness (I have reactive allergic red skin). My scars are rolling like and my texture is still poor.