>>313188924
I'd use proportional editing with "connected only" checked. Use the scroll wheel to adjust the area proportional editing affects while moving verticies around (G).
You can also select multiple vertices, like a line of them on the lower lip, and move those around, or set your 3D cursor to the inside of the mouth and rotate them around that point.
It's not required, but I also like using the Mesh Fairing plugin while working with shapekeys, which lets you easily make areas of the mesh flush with everything else.
https://github.com/fedackb/mesh-fairing