I think that might actually be possible. You can use this technique to make a convincing eggshell texture: https://youtu.be/0iN4fmHFd0A (Not the best video, since it doesn't specify the ratios of ingredients, but it shows the process and someone posted the ratio in the comments.) Then just coat it in a thin layer of something that is waterproof and edible.
I'm guessing that it'd be possible to coat chocolate, peanut butter, or even shaped or whipped cooked eggs (Or raw whipped meringue egg whites with pasteurized eggs.) if you keep them refrigerated and cold in your drink.
I think that might actually be possible. You can use this technique to make a convincing eggshell te