It's certainly worth a shot. That looks like it ought to work no sweat.
I would put some solvent on a cotton swab and dab it around where things look like the pivot, pushing the little levers here and there very gently until the two blades move -- those shutters are very simple things, mechanically, and usually just get dry and stuck. Once it moves even a bit you'll see which does what and it should loosen up.
I have an old bottle of dry cleaning fluid I use for such things -- it evaporates without residue. Try to find something like that.
The main thing is just don't force anything.