So first, a caution against complex colliders... The more colliders you have, the more your game is going to slow down. Now, on to your question.
I'm going to level with you here, I don't think Construct can do what you need it to out of the box. You're talking about weird weighting, and how the heavy end of the egg effects that wobble, and those concepts aren't really in Construct, I don't think. (Someone PLEASE let me know if I'm off base).
That being said, with a complex collider map and some elbow grease, you can simulate that wobble, but not in a really automatic way. Essentially, when the egg collides with the ground (On Collision Enter) you can have the egg rotate using the "Rotate Toward Angle" action and some random numbers, you can have the egg rotate quickly, simulating that shake. It won't be realistic, and you may have to play with the conditions a bit to get it to work at all, but that might be the only way to do it.
Best of luck!