You can create a new folder in that directory and host your images in there.
You need to do this anyway in order to get the favicon working for the customer. Only the standard (locked) folders get updated with new releases, your custom one will be left alone.
I usually call it 'assets' and then add a subfolder 'img', because at application level, the favicon is always 'img/favicon.ico'. So at the Configuration record, set your Favicon Path field to 'assets'.