That's an awful set of constraints, but what you're asking is possible:
UPDATE tabl SET col = CONVERT(nvarchar(10), CAST(col AS datetime), 101)
The 101
at the end is the appropriate date style grabbed from this page: http://msdn.microsoft.com/en-us/library/ms187928.aspx
The result is, though, that you'll have dates that are difficult to order and are format ambiguous. Storing as a datetime
is the respectable thing to do.