As many people may have probably guessed, whenever you extract Yoshi's texture parts, you'll also get a CLR0 file that apparently affects what his egg would look like when you use his shield.
Anyway, this file is called FitYoshi00EggGuard.CLR0, and I'm not too sure about how the people that edited Yoshi were able to alter the appearance of his egg. I do know that the file affects Yoshi's egg shield in some way since his only indexed texture (Yoshi_Egg) hardly does anything to the egg.
Register's White Yoshi
(http://i34.photobucket.com/albums/d131/ChronoExplosion/Texture%20Hacks/th_al_090525_1442binout.jpg) (http://s34.photobucket.com/albums/d131/ChronoExplosion/Texture%20Hacks/?action=view¤t=al_090525_1442binout.jpg)
NICKtendo DS's Billy Hatcher Yoshi (Stack Smash)
(http://stacksmash.cultnet.net/wp-content/uploads/2009/07/egg-150x150.jpg) (http://stacksmash.cultnet.net/wp-content/uploads/2009/07/egg.jpg)
I did that once. I made his egg red and white. It is kinda simple to edit.
I'm actually starting to understand the whole story about the egg shield. Yoshi's CLR0 file is actually used to show the player how much time is left before the shield breaks, while his egg texture part (Yoshi_Egg) controls what is shown on his egg.
I've never edited Yoshi's egg texture before since I lacked Photoshop when I did my first set of Yoshi textures. This is probably why I was so confused about the egg textures.
Feel free to lock this thread Mods since I've pretty much answered my own question.