He will constantly second guess everything while he is still in contact. Withdrawal of her will be hard enough, and if he has contact it will be near impossible to have feelings for you.

Him trying to get out of the situation is a good sign.

Yes, you could not sign off on the store until you have something more concrete about the ending of the affair. Have him write a letter to you that you will read and approve and send YOURSELF. You could also talk to her to make sure it is done. Whatever it takes to be certain. If he is done with her, he won't mind this.