The Cold War did involve direct military conflict between the super powers. Those confrontations were just contained and covert and in many cases are still not publicly acknowledged. From what we do know about such direct cold war confrontations, mostly coming from Russia David French's numbers are pretty close. However, given many such actions are still unknown to the public, there is reason to suspect his numbers are low.

The Cold War was not called cold because it didn't involve shooting wars. It was called cold because both super powers took measures to cover-up their direct involvement in wars in which the other was publicly participating. Both parties struck at each other clandestinely, mostly with weapons and training but also with military participation.

The Cold War involved dozens of proxy wars in which millions of people died. The most famous of these proxy wars were Korea, Vietnam, and Afghanistan but there were dozens more. In some of these proxy wars it was not uncommon for US and Soviet militaries to come into direct military conflict for years at a time. If these are the deaths that you are speaking of the answer is not entirely understood because for fear of escalation neither side acknowledged their casualties or even their involvement. Public knowledge of those incidents are thus limited even today.

Just in the Korea War alone the Soviet Union lost 282 to 316 pilots and airmen in struggling with the American Air Force for air superiority over North Korea.

Soviet Combat Losses

282-316 Soviets Lost in the Korean War(1950-1953)
13 Soviets Lost in Vietnam (1964 to 1973)
60 Egypt 1956 - 1974(!)
35 Syria 1956 - 1991(!)
(!) Unknown American involvement.

Korea and Vietnam were wars in which the United States was fighting and the Soviet involvement was clandestine. During the Cold War their were many such wars, and many where the Soviets were publically fighting and the American Military involvement remains classified. Take Afghanistan for instance where the Soviets lost about 14,453 soldiers. The full story of American involvement remains classified.

Korea

SOVIET CASUALTIES DURING THE KOREAN WAR (1950-1953) According to declassified Soviet Records, throughout the Soviet Union deployed 12 divisions of the Soviet Red Airfare – numbering an over-all figure of 72,000 combat (and supporting) personnel throughout the entire three years of the war – peaking with 26,000 operating in 1952. During that time, Soviet pilots shot-down 1097 enemy planes, and the Soviet Anti-Aircraft Artillery shot-down 212 enemy planes. The Soviet Airforce lost 335 planes and 120 pilots. Over-all, the full Soviet casualties are listed as 282 people.

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Russia's Secret Operations
In the Korean War the Soviet Union deployed the 64th air defense corps, with over 300 fighter jets, over 400 pilots, 2 artillery air defense divisions, and ground staff -- up to 40,000 in all. The 64th was given the task of challenging US air supremacy over the Korean peninsula, but pilots were ordered to fight only defensive battles and not to fly near the front line. From 1950 to 1953 the 64th lost 335 fighter jets and 125 pilots. Overall, Russian casualties in the Korean War are estimated at 316 dead. The US lost some 55,000 men and 1,182 airplanes.

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Russia's Secret Operations

Vietnam

From 1964 to 1973, 6,359 Soviet generals and other officers "visited" Vietnam. Soviet-guided surface-to-air missile (SAM) regiments were deployed to encounter US warplanes. Thirteen Soviet servicemen were lost in action during these years. In Indochina the US lost over 60,000 men and 8,612 aircraft.

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Russia's Secret Operations

Egypt (1956 to 1970s)

In Egypt Russia lost 25 military advisers and 35 combat personnel.

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Russia's Secret Operations

Syria (1956 to 1991)

In Syria and accompanying Syrian troops into Lebanon from 1956 to 1991, Russia lost 3 generals, 39 other officers, 1 non-commissioned officer and 1 private.

Other Cold War Proxy-Wars and total casualties.

Cold War and War on Terror Casualties and De-Escalation

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Conflict                                        Total Cold War Casualties          
================                               ================        
Greek Civil War                                 158,000            
Executed in East Germany                          3,000             
Hungarian Revolution                              6,222–6,722               
Korean War                                        2,469,287–3,272,955             
1945–49 Chinese Civil War                         2,500,000–6,000,000               
Iranian Revolution                              200–300          
Guatemalan Civil War                            200,000           
Congo Crisis                                    100,000          
Cuban Revolution                                  5,000         
Bay of Pigs Invasion                              4,198           
Dominican Civil War                               2,825             
1965–66 Indonesian Genocide                     400,000–3,000,000          
Vietnam War                                     966,000–3,812,000         
Cambodian Civil War                             240,000–300,000             
Cambodian genocide                            1,700,000–3,000,000             
Laotian Civil War                                20,000–62,000            
Hmong genocide                                  100,000           
Degar genocide                                  200,000          
Boat people                                     200,000          
Reeducation Camps                                95,000         
Foreign Intervention In Indochina Wars           65,425       
Operation Condor (3,000 Pinochet, 13,000 Vidella, et al.)          
                                                 60,000–80,000           
Yom Kippur War                                   10,822–21,601           
Ogaden War                                       14,119         
Menghistu Haile Mariam Crimes Against Humanity  430,000–1,500,000          
Angolan Civil War                               500,000           
East Timor genocide                              60,000–308,000           
Soviet Afghan War I                             500,000–2,000,000         
=====================================================================          
Low End Total Casualties                      10,580,098           

Sources:
Russia's Secret Operations
Soviet Casualties During the Korean War(1950-1953)
Wikipedia: Greek Civil War
Cold War and War on Terror Casualties and De-Escalation