Have been down the road where it looks like it doesn't matter what you say or do....the problem with the papers are there ready to go is, delaying it basically ticks her off to no end. signing it basically means you accept the fact that you are not controlling her. For one...big weight off her shoulders and she feels she can breath. Two...you get to regroup, think about what to do next with YOUR life...not hers. And three...you have to keep a positive attitude. If she has any soft spot that will warm up to you in the future...it will be when she sees you and hears you...so if it is a positive interaction then it can only go in favor for you.
As previously said by others, the big D is not the end....but the beginning. Learn from your mistakes..don't repeat them and move forward with your life....you'll be surprised....believe me.