I have the same problem
I've used Gentleman's Refinery unscented shave cream with no irritation. My favorite though is Provence Sante Green Tea soap. I know nothing about ingredients but here they are:
Key Ingredients: Potassium Palmate, Sodium Palmate, Potassium Palm Kernelate, Sodium Palm Kernelate, Glycerin, Water, Talc, Fragrance, Butyrospermum Parkii (Shea Butter) Fruit, Sodium Chloride, Titanium Dioxide, Palm Kernel Acid, Tetrasodium Etidonate, Pentasodium Pentetate.
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