The shell of an egg is predominantly calcium carbonate and will thus dissolve in acid. There's a common kids experinebt that involves dissolving the shell of an egg in white vinegar to make it bouncy. Leaving the egg in the vinegar for an extended period also pickles the egg white, making it increasingly rubbery and bouncy
You could experiment with different household acidic liquids (vinegar, lemon juice, soda water) to find the time required to dissolve or weaken the shell sufficiently that it breaks silently or cuts with scissors, without being in the acid for so long that it becomes flavoured (though who knows, you may come to like lemon eggs!) You probably only need to dip one end of the egg rather than immerse the entire thing
You could additionally consider changing how you eat it (I'm presuming you fry, or scramble); boiling an egg then rolling it around in the base of the pan, under the water will quietly break the egg shell into fine pieces, squeezing one end then causes the boiled egg to pop out the other - it's a temporary measure; babies sleeping patterns don't remain fixed for long (in a few month's time things will be different).
There may also be periods where she is in a deep sleep and breaking an egg normally doesn't disturb her. Sleeping runs in cycles, and my experience is that a child's cycle is about 30 mins long whereas an adults is 45 to an hour. People are most susceptible to being woken when in the lighter dreaming phases of sleep