Hello there! Many of us here started soaping because of skin problems - our own, or those of our loved ones, or both. So you are in good company.
You can certainly try a high-shea bar, but they do need a long cure. Also, shea is not usually the best oil or butter to use when making a soap for someone with eczema. The qualities of the butter are changed as it goes through the saponification process, i.e., becomes soap, and it can be a skin irritant for sensitive folks.
I recommend starting with one or both of these formulas:
1. Castile bar soap made with 100% olive oil. You can search the forum for "Zany's No-slime Castile" to find a recipe that doesn't require a one-year cure like normal Castile soap will need.
2. A high-lard bar soap. The composition of lard is very similar to the oils on human skin, and it seems to retain many skin-loving properties even after becoming soap. My family members with eczema love this soap - it is so gentle! They are able to tolerate it with about 10-20% coconut oil, which helps it lathers better. But to be on the safe side, you might want to start with no coconut oil at all. You can try 75% lard, 20% olive oil, and 5% castor oil. This soap will benefit from curing for at least eight weeks. The lather gets a lot better as it cures longer.
For either recipe, keep it unscented for now, since many scents (even essential oils) are skin irritants. You can increase lather by adding some form of sugar. I love using goat milk powder for that. Powder is easier for a beginner than liquid goat milk, and the sugars in the milk powder will help your soap lather a bit better. Colloidal oats can be nice, too. However, some folks with eczema can't tolerate either of those ingredients.
It can be quite a long road of experimentation to find out what works for your loved ones. Then again, some people find that almost any handcrafted soap is fine for their skin - more because of what it doesn't contain, rather than what it does. You could always try purchasing a bar or two of high-OO or high-lard soaps, and see how they do with it. Then you can make a similar soap, knowing that it is likely to work for them.
Good luck, and happy soaping!