I see CRE drives all the time with pets but I think as a company driver it may just be one of those things you just don't mention. I had a student go into the relief and recovery fleet and he recovered tractors that had fur wall to wall in the inside. I think you will be fine as long as you dont bring to much attention to yourself.
England policy is no pets for company drivers. If you decide to risk it better be careful in Salt Lake and Burns Harbor as there are a lot of kissbutts that will rat you out to curry favor.