Change the direction a single view puppet is facing?

Hi all. Not asking about how to do turns or parallax or anything of the sort, but if I'm using a particular puppet that only has one side view rigged (for example, one of the Puppet Maker templates, like Cowfolk), the characters only face one direction.

Can I horizontally flip the entire puppet rig so the character faces the opposite direction (so, for example, I could cut between two puppets facing/talking to one another instead of them both looking off to the same direction)? I don't need a turn and I dont' need it to happen "on camera", I would just like to be able to choose whether a single angle character faces left or right.

Thanks!