The OP clearly states that armies really only use roads and there is no purpose in veering off of them even cutting off a few miles for a journey. I am sure heroes are not bound to this rule or the things that try and stop them, nor are some creative movements and the orders that stop such movements, nevertheless, we should just assume that an army is crossing a road at all times.
From this mock map I've created, from the original map, these are the only two routes out of the Dwarvish realm into the realms of men. The north crosses into Harlond, and north of it is Mithlond, it also crosses back into the other route, which has an elven army station over the border crossing.
So it is without doubt that if the Dwarves of the Blue Mountains wish to make any military movement, they must engage in cordial relations. They may be their own realm but greatly reduced they are, and just as well if they wish to use Lindon roads, they can at least contact their administrator or they are welcome to build their own.