I think ill hand her back my ring when she hands me the papers. that will symbolize to me the official dropping of the rope.
I wouldn't do that - I see what you're TRYING to do, but it almost seems spiteful and vindictive. If you don't want to wear your ring, take it off, put it in a drawer, and go from there.
I still wear my ring - My W has never made a comment about it, and I even play with it all the time.