I know it's probably too late to reply to this but I am originally from Green City, Missouri, and my 3x great-grandfather was a SHAW.
Joseph SHAW b. 1795 - d. 1860
md. Louisa MARTIN on 30 Dec 1847 in Sullivan County, Missouri
I haven't been able to find any more on either of their parents or siblings. But I do have information on their children.
If you do get this message, I'd love to hear back from you.
Rachael (McDonald) Gokboga