A fishing riddle is:
   
Q: What did one fish say to the other fish?
A: Keep your mouth shut and you won’t get caught.
   
The riddle was printed in the Courier-Times (Bristol, PA) on January 7, 1958.
 
     
Newspapers.com
7 January 1958, Courier-Times (Bristol, PA), “Riddles” by Carol Mangiaracina, pg. 17, col. 3:
What did one fish say to the other fish?
Keep your mouth shut and you won’t get caught.
 
Newspapers.com
24 March 1963, Indianapolis (IN) Star, “Riddle Box,” sec. 2, pg. 9, col. 5:
What did one fish say to the other fish?
Shut your mouth and you won’t get caught.
 
Newspapers.com
18 October 1986, Lexington (KY) Herald-Leader, “Just kidding,” pg. C6, col. 2:
What did one fish say to the other fish?
Keep your mouth shut and you won’t get caught.
 
Google Books
Laughs, Hoots & Giggles
By Joseph Rosenbloom
Illustrated by Joyce Behr
New York, NY: Sterling Publishing Company
1987
Pg. 26:
What did one fish say to the other?
“If you keep your big mouth shut, you won’t get caught.”
     
Google Books
The Good Sports Joke Book
By Paul M. Miller
Uhrichsville, OH: Barbour Publishing
2004
Pg. 87:
What did one fish say to the other fish?
“If you keep your big mouth shut, you won’t get caught.”
 
Google Groups: alt.humor
Kid’s Puns o the Weak 05-11-04
Stan Kegel
May 11, 2004, 2:43:20 PM
(...)
What did one fish say to another?
Keep your mouth shut and you won’t get caught. (Isabelle, 4)
     
Twitter
Amanda
@amandajcameron
What did one fish say to the other? “If you keep your mouth shut, you won’t get caught”
3:27 AM · Nov 30, 2009·Twitter Web Client
 
Twitter
Old Glory Enterprise
@lifecount06
Q)what did the big fish say 2the little fish? A)“if u keep ur mouth shut we won’t get caught”(knee slapper no,cute little joke,yes.) jp
7:24 PM · Dec 15, 2011·Twitter Web Client
     
Twitter
Express Employment
@ExpressMcD
Joke of the Day:
Q). What did one fish say to the other?
A). If you keep your mouth closed, you will not get caught.
#Joke
7:25 PM · Dec 29, 2013·Facebook
 
Reddit—Jokes
Posted by u/jak3602 January 31, 2014
What did one fish say to the other?
Keep your mouth shut and you’ll never get caught.
 
Twitter
Jimmy RevJim Olsen
@mybuddyjimmy
What did one fish say to the other? Keep your mouth shut and you’ll never get caught. #LaughoftheDay
8:12 AM · Feb 27, 2021 from West Des Moines, IA·Twitter for iPhone