Yes, you can. Hexes are supernatural at will abilities. But some of them specify that you have to do something for hex to work. If your new base form cannot do that task you cannot use that hex
I believe you can cackle/chant if that animal/vermin is capable of doing something similar. Monkey can do it, spider cannot. That's how I see it.
But you can find your way around it. :) Namely ring of eloquence - that definitely grants you ability to chant and probably also cackle (table variations may vary).
Also you can cast spells while in beast/vermin form if you can meet spell requirements: Material, Verbal, Somatic. Eschew materials, Silent spell (or ring of Eloquence), Still spell takes care of that.
And I'm sure you would be interested in this archetype: Bouda witch.