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Is there a way to "clip off" the white borders of the maps
Yes, there is.
For paper map scans you would normally start with "Crop Image Margins", but this often does not suffice.
The more complex clipper is called "Transparent Margins" and it works with as mask that you shape yourself. It starts with a rectangle but you drag the points and add more as you like to fit the edges of your map.
"Transparent Margins" can be set before and after georeferencing. If set afterwards, georeferencing information will not be lost!