Nice sketch. You've certainly already realized that there are several ways to accomplish this. The best solution I can think of would be to clamp down the length of wire that is to remain straight and have flat hinged arms that swing to fold the ends that are to be bent. These arms can be attached to segments of pulley and a cable so that the piston always pulls tangentially. All you would have to do is figure out what radius of wheel would produce the desired 90$^\circ$ motion with your 200mm movement.
However, that's a fair amount of construction, so if you were hoping for something simpler and similar to your current idea, the wire should be clamped to the moving assembly so it doesn't flex out. The piston's part should be flat and run the whole length of what needs to remain straight. I suppose that's obvious, but I'm not sure by your diagram if you were doing otherwise. It seems to me that you're trying to press the wire into a form that will bend it, rather like a stapler. I would go with a gentle curve that begins contact at the edge and draws in until it only allows enough space for the wire to be bent as you want. It would look something like this:
I guess you'd have to make some adjustments for living in 3 dimensions and all that, but that's exactly why I'm not an engineer. Hope this helps!