Thanks guys. The first 4 digits are
9017 and it is in the current list as
Kindle PaperWhite 2 (2013) WiFi (4GB).
I have had a look at the snapshots but have no clear idea which one(s) I should use. I'd be muchly grateful if someone could give me the link(s), and I will try and take it from there.
As I have said the main problem is that the BIN files do not stay on the Kindle once the USB is disconnected. It is almost as if the device has some sort of anti-malware on it.