Looking around various churchyards and cemeteries may be very time consuming. Probably the better choice is to contact the bereavement service of Plymouth City Council which covers several cemeteries and crematorium. Additionally you could ask for a search at Ford Park Cemetery [now a Trust a charge of £10-50 for a search http://www.ford-park-cemetery.org/index.php/cemetery-services/gave-searches] and Drake Memorial Park a lawn cemetery with metal name plaques at Saltram, Plympton. You will have to pay for searches [£10 for PCC search] but at least they will supply a plot reference which could save weeks of searching on foot. Within Plymouth there are four cemeteries, four closed churchyards and two crematoria.
https://www.plymouth.gov.uk/birthsmarriagesanddeaths/deaths/burialandcremation/cemeteriesandcrematoria/cemeteriesandcrematoriafeesandcharges
Drake Memorial Park has an online search facility http://www.drakememorialpark.co.uk/burials/search.php