Fixing Recessed Block Out Roller Blinds

We have a block out roller blind that is installed into the recess of our window. The blind follows a vertical track.

Problem - The string/chain has come out and we have no idea how to put it back! The blinds are currently all the way down.

I have tried threading it back but I can't seem to loop it back around. The solutions we have seen so far involve taking the blind down but this particular blind is glued in (some sort of bonding agent?).

Is there an easy way to fix without needing to take the blinds down and apart?

The photos below show a similar blind (but working).

Bump - Is this the right section of the forum to ask?

on most of those blinds you pull/push one end up/down so the fixing pin comes out from the fixing bracket, then the blind can be removed.

Quite often the mechanism simply push-fits into the blind roller and can be replaced.

If you can't do that then you'll have to insert an end of the knobbly cord into the mechanism and wind the roller by hand so it drawns the cord round the cogwheel inside the mechanism.