If your going to have a stage hand standing behind the flat, anchor a piece of 40x20mm timber across the rear of the door.
Make sure that the piece of timber extends past the frame and you can use that as a handle to open and close the door.
Just hang a piece of cloth/backdrop so the door operator is hidden from view. And maybe a lack of lighting behind so the door operator isn't in silhouette.
If it's not centre stage, you might even be able to operate it from the wings.
Or fit a weight and pulley to it, to close it, and open it from the side with fishing line, no catch needed.
The length of the timber will give you an advantage over the weight.
The weight can be a bottle of water, just fill it till it works, using a Bottle with a handle on it so you can hang it securely.
2 Litre fruit juice/Milk bottle would probably do it, won't need much.