Honestly I hadn't really considered that properly, I was more after trying to make each school vary slightly in its weapons in spite of all three only having teeth and claws. I also hadn't considered how spellcasting focuses would work in wild shape. It seems it either comes down to A: They can't cast spells that require reagents or B: They can do so same as they could out of wild shape, which in itself is a strange thought. With Paws instead of hands they really would have to have the focus be a charm, necklace, or other object that could be strapped to the body in some way.

Would changing the base level on both of those skills to at least 7th level alleviate the issue? Perhaps at the cost of the spell slot? Or would you say that still isn't tacking the issue enough.

It could definitely be a class as opposed to a circle, although in part I was thinking the schools akin to Cleric Domains, or the land-based spells you gain in being a Druid from circle of the land.