I would not be too quick to rule out Walsall. Look on FreeBMD and you'll find a birth of Thomas Kenny in Dec 1862 for Walsall and there's no trace of one in Cheshire. Admittedly birth registration was not compulsory in 1862 as I understand it but I don't believe in coincidence. Have you looked in the 1871 and 1881 census for the family ?