i don't know if this helps on what type of guns, immigration from the US was happening.
The Loyalist Immigration
Many of Québec's new British rulers, content to leave the colony to languish as a quiet backwater of the Empire, were soon forced to accept many thousands of English-speaking, largely Protestant settlers displaced by the American Revolution. Known as United Empire
Loyalists, they were largely political
refugees. Many of them migrated northward not by choice but by default, either because they did not wish to become citizens of the new American republic or because they feared retribution for their public support of the British. For these Loyalists, who eventually formed the core of the colony's ruling oligarchies, Canada was a land of second choice, as it would be for countless future immigrants who came because to remain at home was undesirable, and entry elsewhere, often the US, was restricted.
The Loyalist migration was neither uncontrolled nor unassisted, however. Imperial authorities and military personnel offered supplies to the new settlers and organized the distribution of land. Despite the hardships the settlers endured, their plight was undeniably made less severe by the intervention of government agents, a practice to be repeated in Canada many times.
Throughout the mid-19th century, the colonies — Canada West in particular — returned to a pattern of painfully slow and erratic economic growth. Officially encouraged immigration from
England,
Scotland and even the US gradually filled the better agricultural lands in the colony and bolstered new commercial or administrative towns. The new immigrants were generally similar to that of the established community. But the great Irish potato famine and to a lesser degree a series of abortive European rebellions in 1848 sent new waves of immigrants to North America.