The easiest and fastest thing you can do is to create a shelf just for your mouth animation:
create a new empty shelf and call it "mouth" or whatever you like.
This method uses one material per mouth texture and it is not ideal,
you could use only one material and multiple textures but I want to do a very easy setup.
create a geometry plane for your mouth texture, rename it properly.
Now create a material, input the mouth texture and assign it to your mouth geometry.
Duplicate the geometry for every mouth, rename them, duplicate the materials and assign a different mouth to every geometry.
group the geometries under a parent group and call it mouth_grp or whatever you like.
Parent this group under the face geometry.
Now open the script editor.
Keep it on a side of your screen and select all the mouth geometries at once.
set their visibility to 0 in the channel box.
In your script editor´s top panel you should see something like this:
setAttr "mouth_01.visibility" 0;
setAttr "mouth_05.visibility" 0;
setAttr "mouth_02.visibility" 0;
setAttr "mouth_03.visibility" 0;
setAttr "mouth_04.visibility" 0;
copy this text and paste it in the lower panel.
Now, you replace the first 0 with 1, select the whole script and drag it to your new shelf.
Do the same operation for all the other zeroes, one by one, so in each script only one mouth is visible.
The rig is done, you have a set of shelf buttons that replace your mouth.
If you want you can create thumbnails of your mouth textures and assign them to the shelf buttons
in order to have a visual interface.
Cheers,
D