You never know. Since she was a married woman she, and the baby, would appear under her late husband's surname even if he was provably not the father. The certificate might name him anyway, or no father at all, or you could look up "James Walter" with the relevant details to see if there's another entry under a different surname, which might suggest two different parental surnames on the certificate.
A christening, if you can find one, might potentially be more likely to name the biological father.