An area that became Tenn was originally named Washington County, but that county was dissolved before 1799, which was when the present-day Washington County, NC was formed from Tyrrell County (more land was annexed in 1801 from Tyrrell to Washington). Washington County, NC is on the east coast, south of the Albemarle Sound. It's only relationship to the county that used to exist is that they have the same name.
This site has a brief historical background on Tenn:http://www.tngenweb.org/pre1796/
One problem for you is that a lot of people from North Carolina migrated west and settled in Tenn - they came from all over - there were some who left Tyrrell County prior to 1799, and went there, then more left after 1800 (some from Tyrrell County, some from Washington County). Given the dates you mention, you might have better luck posting a query on the Tyrrell County forum instead of here, since your husband's ancestor was in Tenn before modern day Washington County was even formed. You might want to put a query in at every NC county that was in existence between 1775 and 1800, covering the birth year and the first year you know he was in Tenn. You can find a listing of the dates when counties were formed, and which other counties they might have been formed out of, here:http://www.ncgenweb.us/county-list