I also am very sensitive to chemicals....one of the reasons why I make almost everything I can, including soap. If the soap recipe is followed closely, there will be no traces of the lye left.
Think of it this way. You might pile up all your goat poop, pee, and bedding in a compost pile, let it break down, then work this precious stuff into the soil of your vegetable garden and grow lettuce, cukes, and tomatoes. When you eat the resulting organic salad, you are not eating poop and pee. It has completely changed from something nasty into something wonderful.
Same with the lye in soap.
The first time or two that you make it, it might be intimidating, but press on....it gets pretty easy. If you can measure ingredients, tell temperature on a thermometer, stir, and pour....then cut something the texture of cheddar cheese, you can make soap. If you can safely cook pasta....deal with boiling water and pouring hot stuff without burning yourself....you can handle lye. If you get a little on your skin, it will burn, but then you just run it under cool water and wash it off and it won't even leave a red mark if you are reasonably quick. Do wear eye protection, though.
Oh, and you also need patience...you need to lay the bars out, not touching each other so that air flows around them...until they cure. That takes about 3-4 weeks and you can test it by touching a bar with your tongue. If it still has a little lye, it will "bite" a bit. If not, it will taste like VERY mild soap.
It will be LOVELY to use. You will not need much lotion if you wash your hands a lot with goat's milk soap, if you need any at all. Most people are hooked once they try it.