The Charles Wooderson you are looking for may be related to the family of Woodersons who lived in the Crondall area. Their is a Charles as a child in the family of Jonas and Sarah Wooderson, who were married at Crondall in 1791 but according to the data I have he was born in 1809 and registered at Crondall. To the best of my memory these details were obtained from a parish record stored in Guildford Surrey, which I was searching in 1996/97. Hoever to the best of my knowledge this Charles married in England at Crondall in 1835.
This does not mean that your Charles is lost in the mists of history, as one thing I have found in researching the Wooderson family is that more often than not brothers and sisters gave the same christian names to their children. Thus couysins often had to same christian names. I would suggest to you that it may be possible to find your Charles in parish church records in the Crondall area of Surrey and that these parish registers of births, deaths and marriage are in Guildford. There is a feeling in my mind that most of the Woodersons from Surrey of the 17th, 18th and 19thcenturies are all related and that we may have a common antecedent. I will look for your Charles the next time I go to Guildford.