I wouldn't count on him to do anything. It is very unlikely that he'll do anything to help sell the house. I'd make arrangements to have the work done by a paid crew and then keep the bills for reembursment, if you can afford it. He probably won't read the papers because it is too real.
Signing the divorce papers will mean so much more if you cut the strings of expectation that he will do anything. He isn't going to paint of clean up the house. He also isn't going to hire anyone. If he can't muster up enough to read a piece of paper, doing anything to help sell the house would just be a metaphor to the same thing.