Career: Woodeshick pitched for six different teams over his eleven years in the majors, most of his time came with the Houston Colt 45s/Astros. Although he made 62 starts among his 400+ appearances his most effective work was as a reliever. From 1963 thru 1965 he had over 50 saves in a time that saves were less common than they are now. He was an All Star in '63 and led the NL in saves the following season.
In 1960: He opened the season in the Senators' rotation but after 14 starts and a rough July he went to the bullpen where he was noting if not erratic. He ended the year with a 4-5 record and four saves.
WikiFacts: "He made his last [career] appearance in Game Six of the 1967 World Series against the Boston Red Sox, working a scoreless eighth inning in an 8-4 Boston victory in which he was the Series' record-tying eighth pitcher used in the game by the Cardinals. He was released a week after the Cardinals won the World Series title in seven games." -BR Bullpen page
The Card: This one sports one of the better color combos in the set. And that's the old Comiskey
The cartoon states that Woodeshick intended to work as a journalist after his baseball career but by all accounts that didn't happen. He lived in Houston and was active with the team's alumni and did a lot of local charity work in hospitals.