A popular sign in delicatessens in the 20th century was:
 
“If you don’t smell it, we ain’t got it,”
   
African American vaudeville singer Frankie Jaxon may have added this to the song “Can’t You Wait Till You Get Home” (1929). Printed citations in newspapers date to 1937.
   
               
Wikipedia: Frankie Jaxon
Frankie “Half-Pint” Jaxon, born Frank Devera Jackson (March 3, 1896 or 1897 – May 15, 1953), was an African American vaudeville singer, stage designer and comedian, popular in the 1920s and 1930s.
 
LyricWiki
Frankie “Half Pint” Jaxon: Can’t You Wait Till You Get Home? Lyrics
Can’t You Wait Till You Get Home
This song is by Frankie “Half Pint” Jaxon and appears on the split compilation album Volume 1 (1926-1929) (1994).
 
Spoken: I’m gonna sing you a song entitled, “I’m a delicatessen store proprietor, and if you don’t smell it, we ain’t got it!”
 
Heptune
Can’t You Wait Till You Get Home
(Frankie Jaxon ?)
Transcribed from vocals by Frankie “Half-Pint” Jaxon, recorded July 12, 1927.
From Frankie “Half-Pint” Jaxon, Complete Recorded Works in Chronological Order, vol. 1. 1926-1929, Document Records, DOCD-5258.
Photo of Frankie “Half-Pint” Jaxon
Spoken:
I’m gonna sing you a song entitled, “I’m a delicatessen store proprietor, and if you don’t smell it, we ain’t got it!”
 
1 August 1937, Greenville (SC) News, “This Town Of Ours” by Bill Gaines, pg. 6, col. 1:
You’ll find this sign in Mike Miller’s: “If you don’t smell it, we ain’t got it.”
 
4 September 1937, Chicago (IL) Defender, “Dustin’ Off the News” by Lucius C. Harper, pg. 16, col. 3:
The last one (Southern restaurant—ed.) he approached in his food quest had this sign in the window: “If you don’t smell it, we ain’t got it.”
 
11 July 1945, Trenton (NJ) Evening Times, pg. 16, col. 5 ad:
Sign in a delicatessen store: “If you don’t smell it, we ain’t got it.”
(Trenton Saving Fund Society.—ed.)
 
31 December 1946, Greensboro (NC) Record, “Try and Stop Me” by Bennett Cerf, pg. 6-A, col. 5:
Sign in Second Avenue delicatessen: “If you can’t smell it, we ain’t got it.”
 
June 1949, Hearst’s International Combined with Cosmopolitan (New York, NY), “Winchell’s New York,” pg. 53:
Sign in a delicatessen: “If you don’t smell it, we ain’t got it.”
   
Google Books
The Life of the Party:
Try and Stop Me
By Bennett Cerf
Garden City, NY: Garden City Books
1959
Pg. 342:
And a Broadway delicatessen advertises: “Today only! Homemade imported caviar.” Another sign inside the store warns, “If you don’t smell it, we ain’t got it.”
 
Twitter
Erik Hogstrom
@erik1966lutig
“Menu? This is Booches. If you don’t smell it, we ain’t got it.”—cartoon on wall at Booches. #Mizzou
1:24 PM - 17 Aug 2011
 
Google Books
Don’t Have to Be in Who’s Who to Know What’s What:
The Choice Wit and Wisdom of Sam Levenson
By Sam Levenson
New York, NY: Open Road Distribution
2016 (Originally published in 1979.)
Pg. ?:
IF YOU CAN’T SMELL IT WE AIN’T GOT IT.
Humorous wall inscriptions are more in vogue than ever