“Old soldiers never die—they just fade away” is an old saying that was popularized by General Douglas MacArthur (1880-1964) in his farewell address to Congress on April 19, 1951. Many parodies of the saying have been made.
 
The “fisherman” version is one of the older versions. “Old fishermen never die; they merely fade away” was cited in 1945. “Old fishermen never die, they just lie and lie and lie” was cited in a July 1951 newspaper. ““Old fishermen never die. They Just wade away” was cited in an August 1951 newspaper.
 
“Old fishermen never die—they just smell that way” was cited in an August 1953 newspaper.
 
“Old fishermen never die—they just lose their bobbers” is another popular saying about fishermen.
 
   
Google Books 
Last Leaves
By Stephen Leacock
New York, NY: Dodd, Mead
1945      
Pg. 13:
Izaak Walton, let us pretend to remember, was born in the reign of Queen Elizabeth (1593) but lived so long and so peacefully— old fishermen never die; they merely fade away— that he only passed away at the age of ninety at the end of the Stuart period.
   
20 July 1951, Wichita Daily Times (Wichita Falls, TX), “Furthermore and However” by John Gould, pg. 8, col. 2:
Although he didn’t send it to me, Eugene Sherrod Jr., has one in the magazine “Texas Game and Fish:”
 
Old fishermen never die,
They just lie and lie and lie.
 
25 August 1951, Amarillo (TX) Daily News, “From A to Izzard” by Wes Izzard,  pg. 1, col. 1:
And it was Hub Jones who remarked solemnly at dinner last night:
 
“Old fishermen never die. They just wade away.”
 
1 August 1953, Daily News-Record (Harrisonburg, VA), “Outdoors” by Bruce Slavin, pg. 5, col. 2:
And Finally
A friend of ours recently gave us one of those little varnished, highly decorated boards one sees on sale at vacation resorts. On it was this:
 
Old fishermen never die—
They just smell that way.
 
Now why did he give it to us—Why?
 
21 September 1954, Brazil (IN) Daily Times, “Just Between Us…” by Mack McGinnis, pg. 8, col. 3:
ONE MORE…Now they’re saying that:
 
“Old fishermen never die—
They just smell that way.”
 
1 September 1955, Evening World-Herald (Omaha, NE), “The Town Trumpeter” by Glenn Trump, pg. 6, col. 3:
Another Version
The “old dyers never fade, they just solider away” story we related last week reminded Omahan Bernie Kelley of this sign he spotted in Minnesota:
 
“Old fishermen never die. They just smell that way.”
 
23 December 1955, Evening World-Herald (Omaha, NE), pg. 15, col. 3:
Is That So!—
“Old Fishermen Never Die—
They Just Smell That Way”
By Eugene Burns
(...)
A sign at a drive-in restaurant in the Florida Keys: “Old fishermen never die; they merely smell that way.”
 
31 December 1955, The Times-Picayune (New Orleans, LA),  “Up and Down the Street” by the Want-Ad Reporter, pg. 7, col. 2:
J. G. Bell sends more funny mottoes from Let’s Have Better Mottoes Association.
(...)
“Old fishermen never die; they just smell dead.”
   
Google Books
Phillips’ Treasury of Humorous Quotations
By Bob Phillips
Wheaton, IL: Tyndale House Publishers
2004
Pg. 93:
FISHERMEN
Old fishermen never die; they just smell that way.
 
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@CrispOperations Old fishermen never die. They just smell that way.
3:04 PM - 2 Apr 2015