Cornwallis made his
first-class cricket debut for the
Royal Navy against the
Army at Lord's in 1920. Cornwallis would play three matches for the Royal Navy, the last of which came against the Army, also at Lord's in 1926. Cornwallis also represented
Hampshire in one first-class match in 1921 against
Kent, a match in which his brother
Stanley Cornwallis played for Kent. In his only first-class match for the club Cornwallis was absent in both Hampshire's innings. His brother bowled in Hampshire's first innings, but was himself absent for both Kent's innings and Hampshire's second innings. Their absence was allowed following the death of their brother, Captain Fiennes Wykeham Mann Cornwallis who was killed in the Ballyturin House Ambush near
Gort in
County Galway during the
Irish War of Independence by the
Irish Republican Army. It is likely that Oswald never actually took to the field for Hampshire. ==Family and later life==