People in the psychology industry have long been nicknamed “shrinks.” This has nothing to do with “shrink wrap,” but there are many puns.
 
“Psychologists convention: shrink rap” was printed in The Wall Street Journal in 1992, and “Psychiatrist’s jargon: shrink rap” was printed in the same newspaper in 1997. “A psychiatrist sings you the shrink rap” was posted on the newsgroup alt.humor.puns on February 18, 2001. “If Puff Daddy wrote a song about his psychologist, would it be a shrink rap?” was posted on the newsgroup alt.humor.puns on May 22, 2001.
 
“If a psychologist became a hip hop artist, does it make their music ‘shrink rap’?” was posted on Reddit—Oneliners on October 27, 2018.
 
     
Wikipedia: Shrink wrap
Shrink wrap, also shrink film, is a material made up of polymer plastic film. When heat is applied, it shrinks tightly over whatever it is covering. Heat can be applied with a handheld heat gun (electric or gas), or the product and film can pass through a heat tunnel on a conveyor.
     
16 July 1992, THe Wall Street Journal—Europe (Brussels), “Pepper…and Salt,” pg. 6:
Daffynition
Psychologists convention: shrink rap.
—H.C. Lindgren.
         
18 April 1997, The Wall Street Journal (New York, NY), “Pepper…and Salt,” pg. A19:
Daffynitions:
Psychiatrist’s jargon: shrink rap.
—Arie De Kok
     
Google Groups: alt.humor.puns
“Puns of the Weak” 8/4/00
Stan Kegel
8/5/00
(...)
I was surprised to see my psychiatrist in the audience of the Grammy awards, and even more surprised when his name was read as the winner for best new music genre. It’s called, “Shrink Rap.” (By Anita Gard)
 
Google Groups: alt.humor.puns
Shabby dog story
Pun of the Day
2/18/01
(...)
A psychiatrist sings you the shrink rap.
 
Google Groups: alt.humor.puns
Searching for counseling and psychology humor. .
Robert E. Lewis
5/22/01
(...)
If Puff Daddy wrote a song about his psychologist, would it be a shrink rap?
     
Twitter
Mark Amador
@_Amadorable
Here we go. What’s a Psychiatrist favorite type of hiphop? ..... SHRINK RAP
10:12 PM - 14 Aug 2009
 
Twitter
Kristen Waters
@kristenMwaters
@johncmayer Question: If M.C Hammer was a psychologist, would his music be known as “shrink rap” ? (Thought you’d appreciate this one.)
9:39 AM - 29 Dec 2009
   
Twitter
Dale Knutson
@daleknutson
A psychiatrist and psychologist formed music group called shrink rap
10:52 PM - 24 Dec 2012
   
Twitter
нακʋвαвʏʏ
@hakubabyy
“If a psychologist sings hip hop, is it shrink rap?” #Theshitpeopleintheplanesay #whoidontevenknow #dafuq #berrycreative
11:56 AM - 12 Jul 2013
 
Reddit—Bandnames
Shrink Rap - compilation album of psychologist-themed hip hop (self.Bandnames)
submitted June 11, 2018 by dontnormally
   
Reddit—WordAvalanches
When your psychiatrist gives you a tight warm hug, and talks to you in rhythmic beats. (self.WordAvalanches)
submitted October 7, 2018 by Kauntest
It’s a shrink wrap with a shrink rap
 
Reddit—Oneliners
If a psychologist became a hip hop artist, does it make their music “shrink rap”?
submitted October 27, 2018 by madazzahatter