Found it. If the Brewers need someone to get "injured" so they can call up Woody, Uecker already laid out a solution in his Ford C. Frick speech.
The "we need a player to get injured so we can call someone up for playoffs" situation is literally an old Uecker joke he told on Carson:
“People don’t know this, but I helped the Cardinals win the pennant in 1964. I came down with hepatitis. The trainer injected me with it.”