Archived KimimaruSmash video from YouTube. Original description mostly intact:

By throwing a Yoshi egg near the bottom of Yoshi's shield at a certain angle, it will poke. This was performed on emulator; I don't have a console with me currently, so I cannot test on it.

Looking at hitboxes reveals that Yoshi is intangible during his shielding animation. However, the billboarded egg sprite used for his shield, which I don't know how to remove, prevents the rest of his body from being seen while in shield; it's likely that the rest of his body isn't intangible and the shield covers everything except this specific angle.

Since Polygon Yoshi has a normal shield, it's possible to see that in this animation, Yoshi's body does stick out a bit at the bottom below his head. This is around the angle where this poke works. The property of Egg Toss expanding immediately might make this shield poke only possible with this move, but more testing will need to be done.

Thanks to hydra for helping discover and test.