A squeaky windscreen is one of those annoying and often hard to rectify problems.
There's not a huge amount you can do really aside from trying out another high quality set of blades of giving the windscreen another good clean.
If you're finding that the washer fluid doesn't cause a squeak, why not try diluting some of that and using it as screen cleaner and wiping with a paper towel.
You could always try wiping the blades with this too.