The Williams surname in some areas of Devon is in more frequent use than Smith, recognised as the most frequently surname in England. It is very easy to confuse cousins, uncles [even fathers re marrying] and other Williams families in an area. This is especially so when no middle name was used. Assuming a marriage or second marriage prior to civil registration when certificates became available is highly speculative. However if you have secondary evidence such as entries in a family bible or a will makes it less speculative. Having the trade cordwainer is an advantage but there would be several Williams trading as cordwainers in any given area. Certainly the 1851 and 1861 censuses will help you.

Can you tell us why you think Barnstaple was his area of birth? On the 1851 census there is a pauper former shoemaker born Barnstaple 1788 which could be your man but how do we establish your man did originate in Barnstaple? Also if he was 'a shoemaker all his life' it seems for part of his life c1851 he was on parish relief so may not have been actively in work [although some paupers receiving relief may have worked in parts of the year].