It may be possible to confirm family relationships with Edwin Bunyan by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA test-takers in his direct paternal line.
Mitochondrial DNA test-takers in the direct maternal line:
Jeremiah Smith and Joanna (Dillon) Smith moved from Lancaster Dist, SC, in 1808, I doubt Edwin Bunyan Smith (1810 - 1872) is his son. His birth date conflicts with Wyatt Smith,1809–1894, a known son of Jeremiah Smith and Joanna (Dillon) Smith. I do see other sources with a birth date of 1807- is that possibly correct?