I think the white is usually the thing that causes the allergy. Just give the whole egg. Chances are, they won't be allergic.
Mine had a hard time with scrambled at first so we did hard boiled and she liked that better.
We just did scrambled... I've never heard of separating them. I wonder what the advantage is 🤔
We just did scrambled egg, I didn't split the white vs yolk! But that's not a bad idea. Now I give her scrambled egg with some veggie, and cheese mixed in, like a little omlette kinda.