I'll weigh in on your question, but before I do I want to say that unless you are truly done I don't agree with filing for divorce. It isn't some sort of wake up call or remedy, although sometimes it seems that way to the walk away. You can stay separated, get a life, be happy without him, and moving on without getting divorced. But that's your decision. If you make the decision to divorce I think you told your H that you believe it's over and your done. You will make up his mind for him....to stick with OW.
Okay, in answer to your question. You don't need a mediator. There is nothing to fight about, you said so yourself. As long as you've agreed to everything, all you need is for a lawyer to basically say "the parties have amicably split the joint assets to their satisfaction" and both of you sign off on it. You both don't need a lawyer as long as you're fair. It probably wouldn't cost much. You can pretty much write it yourself and let your attorney put it into legal lingo. That's how I got a divorce and it goes smoothly.
In the end, it's not the years in your life that count. It's the life in your years. Abraham Lincoln
It is hard to fail, but it is worse never to have tried to succeed. Theodore Roosevelt
