Here's another clue. In the 1850 census for New York there is also a Charles Burke born about 1833 but he is listed as being born in NY. Don't discount this because also in the house are a couple of children - surname Moons - that were born in Wisconsin. There were a lot of Swedes in Wisconsin.
The male head of house in that household is one William Burke born about 1810.
This may be nothing but at least it is a line to check into to see if there is anything to it.