What kind of blinds setup do you have? I can’t visualise it.

I have curtain hooks screwed into the outer front of a wooden frame and a bracket securing the blinds inside the frame.

There are two holes for screws that secure the blinds, and if the holes of both line up it might be possible to put them though a curtain hook bracket then through the holes for the blinds, holding them both on together by the same screw. (Obviously you’d want everything to be light. And not sure if it would hold well.)

However I have no idea of relative sizes or how it would actually align.

Plus if your setup is different or you get adjustable hooks where the lower part of the bracket obstructs the gap or the screw doesn’t pass through, I have to think of something else.

I thought this up after trying to find something similar to a double curtain rod hook but with blinds brackets, a combination of the two, however it seems what I was picturing might not exist.

Where this blind in your picture is fixed with the brackets vertically and inside the window frame the one I’m working on is fixed horizontally outside of the window frame and just above so the bottom of the blind reel is the same level as the top, horizontal edge of the window frame.

Unfortunately I’m not on site and can’t get s picture.