I'm sure many others will set you straight on this, but just to get things going:

Generally, there was little or no shantying on navy ships; it was almost exclusively a merchant vessel practice. In the Royal Navy, with their large crews, they would use a drum beating time if necessary, but no singing. On merchant ships, with their small crews, it was essential that they get as much coordination as possible, and that is where the shanty came into its own.

As far as specifically Scottish shanties goes, there's allways "Hieland Laddie," which took a pre-existing Jacobite song and mashed it up with a shanty called "Donkey Riding." (At least, that's what it looks like to me.)

Of course, you should remember that when the shanty was a living practice, there were very few shanties with set words. (There were some, of course.) Each shantyman would make things up about his ship, his crew and really whatever he felt like. I imagine a Scott would sing about things from home as often as any other shantyman.