The comic actor W. C. Fields (1880-1946) was well known for his witty lines about drinking. “I like to keep a bottle of stimulant handy in case I see a snake— which I also keep handy” has been cited in print since at least 1966-67. “Always carry a flagon of whiskey in case of snake bite and furthermore always carry a small snake” was cited in print since at least 1972.
 
The Fields film You Can’t Cheat an Honest Man (1939) contained a gag where a woman hears about snakes and faints; Fields gives her a snakebite remedy (alcohol), but mostly takes it himself. Harry Yadkoe, a New Jersey writer, had given Fields these snake jokes. Yadkoe sued Fields and won $8,000. It’s not known if the two lines (previously cited) are from Yadkoe.
 
       
Wikiquote: W. C. Fields
W. C. Fields (29 January 1880 – 25 December 1946), born William Claude Dukenfield, was an American Actor and Comedian.
Wikiquote: Talk:W. C. Fields
I always keep a supply of stimulant handy in case I see a snake— which I also keep handy.
. Variant: I like to keep a bottle of stimulant handy in case I see a snake, which I also keep handy.
. Variant: Always carry a flagon of whiskey in case of snakebite. Furthermore, always carry a small snake.
 
31 December 1939, Cleveland (OH) Plain Dealer, “How to Make New Year’s Resolutions” by W. C. Fields, This Week Magazine, pg. 6, col. 3:
I washed it (a maraschino cherry—ed.) down with some snakebite remedy that Grandpa always kept in a downstairs closet.
 
22 January 1940, State-Times (Baton Rouge, LA), “Jimmie Fidler in Hollywood,” pg. 20, col. 3:
The one exception is W. C. Fields—a mighty handy man to have around in the event of snake-bite.
 
2 April 1943, Boston (MA) Herald, pg. 10, cols. 6-8:
W. C. Fields in Court
With Snake Bite Cure
LOS ANGELES, April 1 (AP)—Comedian W. C. Fields went to court today, a defendant in a $20,000 suit over a snake story.
 
Fields was sued by Harry Yadkoe, amateur writer and hardware dealer, who contends he offered the snake yarn and a batch of gags for the actor’s movie roles in 1938.
 
Yadkoe alleges Fields never paid for these offerings but that some of the material was used in Fields’ film, “You Can’t Cheat an Honest Man,” and on certain radio shows.
   
26 February 1966, Winnipeg (Manitoba) Free Press, “Richard Purser’s,” pg. 59, col. 6:
This recalls the late W. C. Fields, who said he always kept “snakebite serum” handy. One should never use it unless bitten by a snake, he added, “which I also keep handy.”
 
Google Books
The Time of Laughter
By Corey Ford
Boston, MA: Little, Brown
1967
Pg. 182:
I like to keep a bottle of stimulant handy in case I see a snake— which I also keep handy.
 
17 November 1972, Aberdeen (SD) American News, “Earl Wilson’s New York,” pg. 4, col. 4:
... the late W. C. Fields, who said:
 
“It was a woman who drove me to drink and I never wrote to thank her. Always carry a flagon of whiskey in case of snake bite and furthermore always carry a small snake.”
 
Google Books
The Quotable Drunkard:
Words of Wit, Wisdom, and Philosophy from the Bottom of the Glass
By Steven Kates
Avon, MA: Adams Media
2011
Pg. 223:
“I always keep a supply of stimulant handy in case I see a snake— which I also keep handy.” —W. C. Fields
   
The Weekly Opuscule
FRIDAY, DECEMBER 9, 2011
The Devil Made Me Do It
(...)
On Oct. 4, 1938 a young New Jerseyite named Harry Yadkoe sent W.C. Fields: “some scenes and dialogue for your next picture ‘You Can’t Cheat an Honest Man.’” The film debuted the following year starring Fields (funniest man ever) as Larson E. Whipsnade (with a comedic assist from Edgar Bergen & Charlie McCarthy). Yadkoe was upset about lack of monies for a scene where a woman fainted each time Whipsnade mentioned snakes; booze was then called for and produced, ostensibly to treat the lady, but really just to be imbibed by Whipsnade. A lawsuit ensued. (Yadkoe v. Fields (1944) 66 Cal.App.2d 150) Yadkoe testified that “I sent ... [Fields] this snake story ... [and] some ‘Snake-isms’ [where] ... I have him coming home and ... [he’s] boasting how he conquered the snake, how he beat it wrestling and ... this women hears the mention of snakes and faints, as she faints he gives her a drink of liquor and takes a drink of liquor himself and goes right on talking about snakes and the same thing happens and he takes another drink ...” Young Mr. Yadkoe won eight grand at trial; affirmed on appeal.