There are a number of reasons why you might not find him on the CWGC site. It could be a simple misspelling of the name, or perhaps Frederick was not his first name. He could have been in the Merchant Navy - many MN casualties are not recorded by CWGC. Unless he died while on duty and as a result of enemy action, he would not qualify for inclusion, whereas Royal Navy deaths from accident, illness etc, are included (an injustice!). He could also have died after 31 Aug 1921 which is the cut-off date for CWGC commemoration. Another possibility is that he died after being discharged and of a cause unrelated to his war service, which again would exclude him from CWGC. However, many who did die after discharge of war-related causes were missed by CWGC.
As to local connections, have you looked at the parish registers to see if he appears anywhere? He might have married a local girl, or been a witness at a marriage. Another possibility is that his mother came from the village and moved away when she married. And have you tried the local newspaper archives, this is an invaluable source for tracing people mentioned on memorials.
