a few notes to consider

Though the family lore that has been passed down for decades about the family origin - state that the family is of Welsh descent - it would seem that the current name spelling of "YANCEY" - does not fit well with Welsh linguistics.
Though there are a few possibilities as to how the current spelling could (theoretically)
 have had a welsh origin - nothing yet has been found to really support such theories. 

Thanks to David Brown and Ian King (both British Citizens) and both having "connections"
to the Nanney famiily for their feed back on this matter,

 - Various Notes
  The string of characters "yanc" doesn't exist in welsh words nor the string "cey"
  The letter "Y" in welsh at the beginning of a word has the short "u" sounds as in "up"
The letter "Y" in welsh in the middle of a word has the short "i" sound as in "sin"
  The letter "C" in welsh  is a hard C - as in "CAT"
  No surname has yet been found in current use in America (or anywhere for that matter) with the ANCEY / ANCY / ANCIE component that is known to have been of WELSH ORIGIN. click here
  Interestingly the English word "YANKEE" has been translated to welsh "IANCI" in some cases.  (because the C is "hard") 
  If someone did want to phonetically spell YANCEY in Welsh - the closest thing would probably be "IANSI"
  Also note large million/billion entry databases like rootsweb or familysearch do not return any entries for IANSI
  Also one would think that if the name evolved over time from a name like IANSI there would be more variations in spelling among the earliest Yanceys and their descendants - yet there seems to be only two known legitimate variations of the name among the family of America -  YANCEY and YANCY. - (though there are surely other variations due to mis-recording and mis-transcriptions and the like )
  The notion that people at the port in America spelled a persons name as they heard it - and that forever changed the family name - is for the most part a MYTH. click here
  Note that among the very earliest Yanceys in America - there is a total void of names that are intrinsically very welsh - such as HUGH, RHYS, GRIFFITH etc - names which are common among the Nanney family of Wales as well as being common among some known Nanney immigrants to America.
click here  click here  click here
  There is an ancient estate by the name of YNYSMAENGUIN in the same general area of Wales as the Nanney estate of Nannau that various Yancey researchers have noted.  Various researchers have reviewed record and as of yet no connections has yet been made between  this estate or its residents and the early Yanceys of America.  Note that Ynysymaengwyn would be pronounced "un-iss-uh-mine-gwin".  There is no record of any family ever taking their surname from this estate name. And welsh families with surname from estate names is quite rare - Nanney being one of the few.  click here.

Some additional links below
  16th Century Welsh Names
  Listen to Welsh
  Learn Welsh Video
  Welsh Language
  a welsh movie about a Nanney descendant 
  Welsh immigrants to America - including Nanney descendants
  Some info on welsh immigrants to Virginia
  Competing theories as to Yancey origin.
  Yancey Family Surname Resource Center
  Nanney Archives