Simon, thanks for the advice and extra information. I have a very fine translucent Arkansas stone, was thinking of using that and then stropping on some plain leather.
Paul, thanks for the suggestion, I've watched the Nigel Armitage awl sharpening video, but my diamond awl is ground quite differently to his one (perhaps because it's a Japanese manufacturer?) and so his method is unfortunately not applicable.
As a general point, the Kyoshin Elle diamond awl came lovely and sharp and ready to use from the box.