As well as the "Luna", the FKR-1 was available during the Cuba crisis.
And it looks as if this would probably made it through any contemporary defenses.
FKR-1
Short range cruise missile. IOC: 1960. Year: 1960. Country: Russia. Department of Defence Designation: SSC-2A. ASCC Reporting Name: Salish. Launch System: FKR-1. Total Mass: 2,999 kg. Core Diameter: 1.19 m. Total Length: 8.23 m. Span: 7.01 m. Standard warhead mass: 450 kg. Maximum range: 200 km. Boost Propulsion: Solid rocket. Cruise Propulsion: Turbojet. Guidance: Semi-Active Radar Homing. Maximum speed: 970 kph.