I'm actually the "boss" where I work and I allow one of my employees to work wed and thurs from home.

So long as they do good work, I could care less where they are. So perhaps try telling your boss that you have thought of all the details like meetings, picking a quiet day when its not busy, or telling them that you will guarantee you will be reachable at all times. Sometimes managers that are old school need to be sold on how you will manage their worst fear - doing nothing at home.