The angles on our door frame made it impossible to close the door just by pulling it closed - the door latch would not climb up and we always needed to use the key for closing it. Now this is already the second version I have made of this door latch slide. It is attached by double sided adhesive tape and it works perfectly. The door now closes smooth and noiseless without a key.

Maybe someone can use this by scaling to their needs or just as inspiration for a fairly simple model!