"Chesapeake and Shannon" also refers to events of the War Of 1812-1814, as does a song about Laura Secord by the group Tanglefoot, as well us a number of other songs to be found in Canadian collections.   

The refugees who left the rebellious colonies in the 1770s for the loyal colonies farther north are known in Canada as the United Empire Loyalists. A quick glance at a couple of songbooks I have yields no results but googling "United Empire Loyalists" might turn up something.