Settlement house - side dormer thermal insulation

Our terraced house from the 1960s is supposed to have the bathroom, which is located on the upper floor with a dormer, renovated. Currently, I have removed the old interior cladding to the roof. Between the rafters, I will install compressed felt insulation. The side walls that protrude from the roof are constructed as follows: interior wall of sand-lime brick 11.5 cm, then about 5 - 6 cm of air, board sheathing with copper cladding applied on the outside. I could imagine filling the 5-6 cm air layer with appropriate loose-fill insulation. However, it is not worth having a blowing-in system installed just for this. Or should I rather leave the air layer as it is? Does anyone have experience?
Best regards

We have a similar house and have installed a drywall partition inside with 100mm of [Klemmfilz]. Of course, with foil and so on.