What I think we did last time was get a large lattice like this, which you can get at Japan Home Centre or any hardware store. Cut out any section you need for access to the window handle. Then use binder clips to attach it to the frame, removing the metal part once they're in place. The window will still close.
We now have professionally installed window screens, and that's really nice (except when that particular part timer didn't close them). The cats have gone crazy once and banged into the screen (flying around mid-air) -- I do worry they're not really that strong, but it's very rare they get near them!