Perhaps giving us the reason would help. There might be other options.

Shutters are complete blockout and allow filtered light. Why would you need blind? Photos?

I am trying to block the light out (to a certain point), unfortunately they aren’t complete block out. This is a pick from 5:30am. There’s no room behind the shutter while outside ones won’t work. Blinds aren’t an option due to lack of side space

Looks like they are bifold shutters, so a roller blind would be problematic, as roller blinds are horizontal and your shutters open up vertically . I would install block out curtains over shutters. Both open vertically. Bifold shutters tend not to have the same block out as large blade plantation shutters.

Is this a door or a window?

French Doors and window

If you can’t do curtains I would go to and blind. You can’t hide a roller blind so might as well look nice

Google examples

The trouble is they are bifold shutter doors, I think, you haven’t said whether they are or not. Therefore roller blinds will have to be secured into the wall above the frame of shutters, giving enough room for the blind mechanism to work correctly, and enough room for the shutters doors to be “bi folded”. If you hardly use that door and will only put the blinds down at night time with the bifold closed, then yes, install them. You could encase the roller blinds mechanism in a pelmet to hide. But again that pelmet needs to finished above the doors. Therefore Roman blinds would not work, because they do not retract completely. Unless you had them secured very high on the wall.

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I had the same problem with light lines at first light. Shutters allow filtered light. And I could never get back to sleep  once I was awake, my best sleep is between 3-5am and it was constantly interrupted.