I always put a little bit of bleach in the water I use -- like 1/4 cup in a half gallon of warm water. I have heard of people using a tiny bit of detergent, but I'm afraid it would get through the shell and leave a flavor or odor. I guess a lot of rinsing would make sure it doesn't, but detergent is a surfactant and makes things more porous, breaks down barriers such as the egg membrane and allows things to penetrate.
I guess you could try a tiny bit and see what it does. That "Fit" vegetable wash stuff they came out with a few years ago to clean produce is nothing more than highly diluted, unscented Dawn detergent, and that washes off without leaving any residue or flavor.
I like the bleach, because it kills pathogens and also if there are any dirty spots, they bleach out, leaving a very pristine, clean egg.