Animating a mouth cutout without affecting skin uvs/texture in maya?


I am struggling with something. I am trying to rig up a very simple and low poly mesh with a super low poly texture. As reference think a minecraft head with a 8x8 texture on the front. So I am looking for a way to cut a mouth hole/shape into the face which I can then rig to animate. But understandably if I animate the shape of the mouth the texture around the mouth deforms along with the mouth’s movement and it being a very low resolution texture it’s very distracting.

I am asking the question because I have seen this done before on animations that used blender. Here is a rough example of what I am talking about: Ignore the teeth, as I don’t need that, but there you can see the shape of the mouth changing without affecting the texture around it. Is there a way to do this in Maya because I have been trying to find a solution for quite a while now. I have contemplated using a boolean operation and parenting it to a mesh I can easily see and control and animate, and this technically works, but I can’t imagine this being the most optimized method especially if I will have a scene filled with characters using this rig.

Also I have put this in the rigging section because in my mind it relates more to rigging than the other categories. If anyone is able to help I would greatly appreciate it :).