Creating a 'Screen' that can display images/videos on a character

I'm looking to create a game in which the characters are all very primitive 3D shapes (cubes, cubois, triangles).

On these characters I need to have a screen which they use to display emotion, messages or just cute little pixel gifs. In a somewhat similar fashion to Wrench's Mask in Watch Dogs 2 (shown below)

Previously I've done things like this (showing a video on a screen) through the use of video files, however I worry that in a game with a wide variety of characters (which I hope to have) I will struggle to keep a low file size without having to constantly load video files for each character.

What I'm wondering is, is there a way to do this some other way, perhaps through a shader - that will allow me to display varied and interesting messages/images on a material - or is a video file method the best way to go?

I'd be interested in learning about this, and this mechanic in particular is important to achieve the characterization I require with such primitive character models.

Thanks, and if any more information or elaboration on the feature is needed for you guys to suggest anything, let me know and I'll gladly supply it.