Can I just substitute fresh ube for the "frozen ube, thawed" my recipe asks for?
Frozen ube is usually grated, raw, and packed in liquid. It comes as a solid block of ice.
Frozen ube is easily found in Asian grocery stores. Especially those that carry Philippine products. In my experience it is much easier to find frozen ube than raw. I expect that is why your recipe calls for it.

I haven't personally used fresh ube but from what I've read, grating it will give you all of the color and more flavor than frozen. Grating it would be messy but would also produce quite a bit of liquid that your recipe would require. I fear that shipping fresh ube you would receive a dryer than average specimen in which case you would have to adjust the liquid of your recipe.

Another alternative is ube flavoring. It ships easily and a tiny bit will stain your muffins ridiculously purple.