The monk's Martial Arts feature's benefits all require a monk to be "unarmed or only wielding monk weapons". Even if you're a Way of the Kensei monk, that only lets you add a couple of new simple or martial weapons to your monk weapon list.
The druid's Wild Shape forms all come wielding natural weapon attacks. Natural weapon attacks are not unarmed attacks, nor are they monk weapons, nor are they simple or martial weapons that can possibly be chosen by a kensei.
Therefore, it seems that a beast is never "unarmed", and thus can never use a druid/monk's martial arts benefits even if it wanted to choose to use unarmed strikes instead of its natural attacks.
Is this interpretation accurate? Or can a beast choose not to "wield" its teeth and claws?
If my reading of the rules is accurate, such a blanket prohibition on Martial Arts when one has natural weapons seems overly-restrictive; it would mean, for example, that a Minotaur can never be a monk, since they are "never unarmed."
I am explicitly not addressing the (already answered and very obvious) question of whether animals can make unarmed attacks. I am asking whether they can ever choose not to "wield" their own natural weapons, so as to be able to use martial arts in the first place.