Edwin is a somewhat uncommon name for that time: Only 171 boys named Edwin James listed on freebmd as born 1840-1860 in England and Wales. Of these, only seven were born in Wales in 1848-1852. Try tracing them and their families in the 1851 and 1861 Censuses: those that were enumerated in the 1861 Census would seem to be able to be discounted from your search. Next you could purchase birth certificates (10 GBP + each - not a cheap exercise...) for those you cannot discount, and check freebmd for deaths in period 1848-61 (e.g. a quick look suggests that the Neath boy died at c.3 months old) and purchase death certificates to resolve any remaining queries. This might narrow down the candidates considerably. I've successfully employed this strategy with more commonplace Welsh names - admittedly with some geographical clues as to which county to search in.
Usually, US newspaper obituaries provide quite a lot of information on where people were born, when they emigrated, etc. - but with the caveat that this information was provided by next of kin and may contain misconceptions. Different newspapers might have contained differing amounts of information - its worth checking all the newspapers that circulated in the locality.
By the early C20 many states' death certificates include fields for names of the parents of he deceased. Again, this information is limited by the knowledge of the next of kin who registered the death - I've found children of the deceased having knowledge of their grandparents' names.
US marriage records frequently recorded parents' names.
When the above are combined with US immigration records (as suggested by a previous poster), you may possibly solve this query.
Rowlands observes that James "is very much a surname of south Wales but it is not in the first rank of common surnames. The only area of significant concentration is centered on north Pembrokeshire (Cilgerran 6.3%; Cemais 5.4%) and south Cardiganshire (Troedyraur 5.4%). It is almost totally absent in north Wales."
One factor to bear in mind - how certain is the Welsh connection? James is also a common surname in England.