In my block a previous owner installed a pull down blind on their balcony (not observable from the street or anywhere on the block) by attaching it to an external wall.
At some time it broke. Subsequent owner (who didn’t install it) just asked – hey, can I repair it? and kind strata manager pointed out that by the previous owner attaching it to the common property (external wall) it became part of common property and the owners corporation had to pay to fix it.
Great.
So I’m in two minds. If you ask for permission and get a “yes, it’s OK” it’s all well and good (just keep the correspondence) but if you don’t ask and just do it (as Lady P suggests) it might be easier (and it’s sometime easier to ask forgiveness than permission).
But I second the recommendation that the Owners Corporation do something about your privacy – even if that something is allowing plantation shutters to be installed.
If different units have different window coverings as you mention, then it does seem that external appearances aren’t an issue in your block.