Do Not use shea butter in a soap for someone with eczema (allergies). Shea contains latex properties that can be deadly to some with allergies. Also keep in mind everything on this earth is an allergen for someone. Susie gave good advice. I will add, I am not sure what you are calling eczema, if it is just dry skin, as some call eczema you might be fine with any soap. If it is the type to cause severe allergic reactions I would start with a pure lard soap. Personally I have 3 types of eczema, at least that is how it was classfied years ago and may have changed now, but the bottom line is my eczema has sent me to the hospital more than once. Also I never never say a soap is eczema safe. Stay away from all color and fragrances. I few years ago I had a gal at a farmer's market come up to me and spread her magic olive oil on my hand. It had lavender which I am allergic to. When I told her to never do that to anyone her answer was, "no one is allergic to lavender." That is outright stupid, I have to use a mask when working with lavender and the way my face feels this morning after working with lavender yesterday I am thinking I need more than a mask. I love salt bars because the salt helps stop my constant itching, but now have to use pko in place of coconut oil since I seem to be becoming sensitive to coconut oil. Mostly I use an emulsified salt scrub I make from a coconut free cream soap I make. Another example of what can happen, my daughter just called me and asked if you could suddenly form an allergy to raspberries her face swelled up, her face and shoulders are red blotchy. She is a severe asthmatic but never had any eczema or atopic dermatitis allergies. Sorry nothing fires me up more than someone wanting to make an eczema soap, lotion, face wash etc. Handmade soaps do not help everyone and I am better off with syndet bars and other daughter has to use Syndet bars every soap she had tried break her out. Cetaphil is wonderful if one is not allergic to it. I have much more to say on the subject but will step down from the soapbox now.
Forgot to add that 10% superfat could smear an oil they are allergic to on their skin in the raw form, hence one of the reasons I very low superfat... Many a person has come to my booth asking for an eczema soap for their child and I explain to them the reasons I do not recommend anything, especially for sensitive children, unless they are under doctor care and were advised to try handmade soap and know what the child is allergic to. Told you I have a lot to say...
If not under doctor care I advise them to seek medical care and be very cautious of what they use on the child. Children can be much more sensitive and have severe attacks out of the blue. Okay I am done now