Georeferencing without altering the picture

Hi there,
I have just finished an easy map. I georeferenced a map of Germany and added some location data as dots. It's basically all we need.
But I used a map, which looked like this:

People are used to see a map of Germany like that and due to the georeferencing the map looks different. Is it possible to georeference a picture without altering it? Or to add the points and remove the georeferencing?

You can find the base-image here