Just a perspective. I was watching a group of deer messing around in some hardwoods a few years ago. They were raring up at each other, pawing, just playing around it appeared. Anyhow, a pack of beagles was running a rabbit in a grown up pasture next to the hardwoods. The rabbit ran down the edge of the hardwoods with the beagles shortly hebind it and the deer just spectated curiously from 75 yards away. Never ran or anything.
So, if the dog isn't actually running the deer I wouldn't worry much about it.
I think many overestimate the effect of such things.