okay, so, i did some extra research, by which i mean i looked around youtube to see if sheep even worked this way on legacy console edition. i couldn't find any videos of anyone dyeing a sheep, but i did find something that's probably more helpful: turns out the LCE version of the pack does have custom geometry for quite a few of its mobs, which i've never seen in an LCE pack before. meaning that even if you find a way to do sheep without remodeling them, you're probably going to have to find something that lets you remodel mobs anyway.
also, the base texture of the "wool" seems to be red instead of white, which is not how sheep are supposed to work, but is something 4j unfortunately has a history of doing.