One maybe-possibility is this: I once saw a recipe where the egg whites were beaten into peaks, scooped onto a hot frying pan and a shallow well made in the center, and the reserved yolk slid into the well to cook with the whites to make something that was essentially a fried egg (no extra ingredients), but with a vastly different texture to the whites.
So, if you really wanted, you might be able to separate your eggs, whip the egg whites, adding a (very) little milk or cream as you prefer, and re-assembling your egg when frying. The texture of the whites would be very fluffy and soft, and the yolk would tend to be less done for being added halfway through the cooking (and possibly having extra volume between it and the heat).
The thing is, the milk or cream won't mix well with egg whites unless you really mix it hard enough to change the texture, so you probably would have to mix it frothy and thin to get the milk to mix, then whip it thickly enough to hold together and not run all over the pan. You would likely only be able to use a spoonful or so of liquid in an egg if you don't want to over-thin your whipped egg whites, or make the structure loose enough to deflate. And it would be a lot of effort, for every fried egg you make. On the other hand, no one but you can say whether or not it's worth the effort.