Nothing conclusive, but some information regarding the Walker family that may help you decide on the maker of your butter knife.
The Walkers', as far as silversmithing goes, were an important Chester family, the first of note was George Walker who was apprenticed to Richard Richardson II. George become a Freeman of the City of Chester in 1767 and was admitted into the Chester Goldsmith's Company on the 19th July 1770. He was elected Warden in 1773 and was appointed the Assay Master at Chester in 1791, a position he held until his death in 1809. Following George's demise his son, John, was appointed Assay Master in that same year. John Walker was a silversmith known to make both holloware and flatware, his biggest contribution to his art was the Stand Cup made for the Chester Races in 1817. He was also elected to the position of Sheriff of Chester 1827.
John Walker continued to hold the position of Assay Master until 1840 (it was he who assayed your butter knife), but in that year a scandal was to explode at the Chester Assay Office that resulted in John Walker being tried at the City Quarter Sessions and being found guilty on a charge of falsifying taxation returns. John Walker was dismissed from his post, and the entire Walker family, some seven of them, were thrown out of the Chester Goldmith's Company.
The above may reveal a couple of points. Thomas Walker may well have been one of those expelled from the Company, and if so may well have been the head of a workshop employing other silversmiths (possibly all Walkers'!) and thus likely to have used journeymen's marks. The expulsion may also account for the confusion in the assay offices records regarding the mark of Thomas Walker with perhaps certain records being removed.
In conclusion, the Walker family were very likely to have had inherited skills regarding the manufacture of flatware and if at least seven member of the family were perhaps linked to the trade, then the liklihood of the use of journeymen's marking is strong.