These are Milgard window cranks

We do sell folding handles that are likely compatible with this operator, yes. See our 39-205. Note that this has a hole diameter of 11/32", so you should check to confirm that yours is the same.

You should note, however, that no matter how far down a handle folds, the spline will always be in the same position. That would be the metal stem that sticks out of the operator and is what the handle connects to. This cannot be lowered in any way and as such the handle will always be raised a minimum distance away from the operator. There's just nothing you can do about it. 

That's all to say that you will ultimately need to find a way to mount the shades to make way for the operator, not the other way around.