Most directly, anne, Scottish Independence will lead to a rapid change in Nuclear policy for both the US and Great Britain. It will also surely have an effect on the weight of the UK's voice in International Politics -- as well as Scotland's.
There are going to be consequences. There must be, because this is no longer a world where nations, especially in the Western World, can think of themselves as isolated from everyone else. There are so many connections. An independent Scotland will change the way these connections work. I don't want to say that this will be a bad thing, or a good thing, because no-one knows how things will change after Independence really -- but it won't go un-noticed.
It's a mistake to regard Scotland as cut off from the rest of the World.