“Airplanes may kill you, but they ain’t likely to hurt you” has been credited to baseball pitcher Satchel Paige (1906-1982). The saying means that air travelers are seldom injured; if there’s a (rare) airline accident, the passengers are more likely to die.
 
“Old Satchel’s plug in favor of air travel: ‘They may kill you, but they ain’t likely to hurt you’” was cited in print in 1966.
 
   
Wikipedia: Satchel Paige
Leroy Robert “Satchel” Paige (July 7, 1906 – June 8, 1982) was an American baseball player whose pitching in the Negro leagues and in Major League Baseball (MLB) made him a legend in his own lifetime. He was elected to the Baseball Hall of Fame in 1971, the first player to be inducted based upon his play in the Negro leagues.
 
Paige was a right-handed pitcher and was the oldest rookie to play in MLB at the age of 42. He played with the St. Louis Browns until age 47, and represented them in the All-Star Game in 1952 and 1953. He first played for the semi-professional Mobile Tigers from 1924 to 1926.
 
Google Books
One Fearful Yellow Eye
By John D. MacDonald
New York, NY: Ballantine Books
1966
Pg. 3:
The busy air is full of premonitions, and one thinks with a certain comfort of old Satchel’s plug in favor of air travel: “They may kill you, but they ain’t likely to hurt you.”
 
28 January 1979, Chronicle Telegram (Elyria, OH), “The Quotebag” by Bob Talbert (Knight-Ridder Newspapers), Sunday Scene, pg. 11, col. 3:
SATCHEL PAIGE, legendary baseball pitcher, on air travel: “They may kill you, but they ain’t likely to hurt you..”
 
Google Books
Hoyt S. Vandenberg, the Life of a General
By Phillip S. Meilinger
Bloomington, IN: Indiana University Press
1989
Pg. 1:
Airplanes may kill you, but they ain’t likely to hurt you.
Satchel Paige
 
MLB.com
Paige family remembers Satchel
Legend’s 100th birthday anniversary is celebrated
By Justice B. Hill / MLB.com | 07/08/06 9:58 PM ET
KANSAS CITY—At the table with Robert Paige were his siblings. His sisters Lula, Rita, Caroline and Pam were there. His little brother Warren was at the table as well, and throw in his nephew Michael, and Robert Paige had his father Satchel’s present and future at his side.
(...)
Or airplanes: “Airplanes may kill you, but they ain’t likely to hurt you.”
   
17 July 2010, Tribute-Star (Terre Haute, IN), “Cryptoquote,” pg. B7, col. 1:
Yesterday’s Cryptoquote: AIRPLANES MAY KILL YOU, BUT THEY AIN’T LIKELY TO HURT YOU. — SATCHEL PAIGE