I had made the connection between my wife and my cousin, and originally figured that she was the wife's 6th cousin. However, there was a logic problem with one of the common ancestors, William Henry Hawley. At this time I cannot remember the exact problem, but with a careful comparison of records at FamilySearch and also FindaGrave, he was connected in a different way to the lineage.
The common ancestor changed from Henery Hawley (1767-1826) * Mary Woodin (1771-1838) Married 17 Mar 1799
Joseph Hawley (Mar 1602 - 20 May 1690) * Katherine Birdsey (1626 - 25 Jun 1692) Married 1646 
This brings us in time to the earliest white settlers of New England. Elias Sill Hawley of Buffalo, New York, compiled a comprehensive HAWLEY genealogy over 40 years of research on descendants of Joseph Hawley of Stratford, Connecticut, and published THE HAWLEY RECORD in 1890. This has been posted online at RootsWeb at THE HAWLEY RECORD. They have an official homepage as well - Society of the Hawley Family.
However, the notation at FindaGrave gives good information about the early Joseph Hawley. According to this he came to Boston in 1629, but it doesn't say how or from where. These questions then led to an examination of early days of New England and the Mayflower (1620-1621).
I used the site Olive Tree Genealogy website that provides a list of early ships (http://www.olivetreegenealogy.com/ships/tousa_neng.shtml)
There is no Hawley listed as passenger or crew on the Mayflower according to http://en.wikipedia.org/wiki/List_of_Mayflower_passengers. There are some names that do appear that are of interest and will be addressed later.
The next ship is the Fortune( 1621) to Plymouth. Again we turn to Wikipedia, and again we see no Hawleys. But there are names to explore further.
The next ships are the Ann and the Little James - England to Plymouth 1623. Again no record on Wikipedia.
The same applies to the Winthrop Fleet 1630.
I ended my search here. There does exist a Wikipedia page for him and states "The Curtiss Genealogy of 1903 states that Hawley sailed to America in the ship Planter in 1635".
So the original information may have been incorrect, but then this would also appear to be as well as an examination of the passenger lists for this ship at Olive Tree Genealogy, for both 1634 and 1635 voyages, do not mention him.
The search will go on some other time...........
..........but there was some success elsewhere.