I can tell you that the rated voltage of the Peltier Effect unit is likely to be your supply voltage as for efficiency there will be minimal loss in the controller. Surprised to learn that they would use a controller, maybe it just switches on or off? You usually need to get as much as possible out of a Peltier Effect fridge, they are normally described as "Coolers" rather than fridges. Come to think of it, though, I DO have one somewhere with a slider control.
Did you know that you can stack the Pelter units to improve efficiency? I tried as many as three, one behind the other. Divided the current by three, and slightly better cooling. Bit messy fitting them, though, with the heat sink compound between the layers and things sliding around.