This was brought to my attention by someone else so I don't know how great the risk is. Barometric dampers are never used on wood stoves from my understanding because they provide the ultimate source of oxygen to feed a chimney fire. I see you stated you'll be installing it for the coal stove.
Even though you're burning coal at this point the concern there is if any creosote build up from the wood catches you're going to have one hell of a problem on your hands.
Now I haven't heard of this actually happening but I'd imagine its certainly possible.
Having said that chances are you're going to give up on the wood idea pretty quick. Most people do after the first season.