I compiled a list of #1 singles, with the Lowest Charting on Hot 100 Airplay / Radio Songs at the time they went #1. This is based on their charting there, not the audience impressions as that'd be impossible to find for every #1.
I primarily did every single song that wasn't Top 20 Airplay at the time it went #1, and this from 1991 onward (when they start using Nielsen Soundscan).
#1's with Lowest Airplay Peaks:
Baauer - Harlem Shake (N/A on Airplay) [March 2-30, 2013]
Eminem - Not Afraid (N/A on Airplay) [May 22, 2010]
Taylor Hicks - Do I Make You Proud (N/A on Airplay) [July 1, 2006]
Carrie Underwood - Inside Your Heaven (N/A on Airplay) [July 2, 2005]
Fantasia - I Believe (N/A on Airplay) [July 10, 2004]
Clay Aiken - This Is the Night (N/A on Airplay) [June 28, 2003]
*2Pac - California Love (N/A on Airplay) [July 13, 1996]
*Toni Braxton - Let It Flow (N/A on Airplay) [July 27, 1996]
*2Pac - How Do U Want It (#73 on Airplay) [July 13, 1996]
Coldplay - Viva La Vida (#65 on Airplay) [June 28, 2008]
Miley Cyrus - Wrecking Ball (#58 on Airplay) [September 28, 2013]
Ke$ha - We R Who We R (#49 on Airplay) [November 13, 2010]
Britney Spears - 3 (#49 on Airplay) [October 24, 2009]
*Elton John - Something About The Way You Look Tonight (#46 on Airplay) [October 11, 1997]
Britney Spears - ...Baby One More Time (#40 on Airplay) [Janury 30, 1999]
Kelly Clarkson - A Moment Like This (#40 on Airplay) [October 5, 2002]
Kelly Clarkson - My Life Would Suck Without You (#38 on Airplay) [February 7, 2009]
Eminem - Crack A Bottle (#38 on Airplay) [February 21, 2009]
Celine Dion - I'm Your Angel (#38 on Airplay) [December 5, 1998]
Katy Perry - Part Of Me (#36 on Airplay) [April 21, 2012]
Divine - Lately (#32 on Airplay) [November 28, 1998]
P!nk - So What (#30 on Airplay) [September 27, 2008]
Puff Daddy - Can't Nobody Hold Me Down (#30 on Airplay) [March 22, 1997]
Avril Lavigne - Girlfriend (#28 on Airplay) [May 5, 2007]
Maroon 5 - Makes Me Wonder (#25 on Airplay) [May 12, 2007]
The Notorious B.I.G. - Hypnotize (#25 on Airplay) [May 3, 1997]
Puff Daddy - I'll Be Missing You (#25 on Airplay) [June 14, 1997]
Rihanna - Disturbia (#24 on Airplay) [August 23, 2008]
Jennifer Lopez - If You Had My Love (#24 on Airplay) [June 12, 1999]
Britney Spears - Hold It Against Me (#23 on Airplay) [January 29, 2011]
Bone Thugs-n-Harmony - Tha Crossroads (#23 on Airplay) [May 18, 1993]
*Elton John - Candle In The Wind 1997 (#23 on Airplay) [October 11, 1997]
Monica - The First Night (#23 on Airplay) [October 3, 1998]
T.I. - Live Your Life (#22 on Airplay) [November 15, 2008]
Will Smith - Gettin' Jiggy With It (#22 on Airplay) [March 14, 1998]
Blackstreet - No Diggity (#21 on Airplay) [November 9, 1996]
*Elton John's #1 was credited as "Candle In The Wind 1997/Something About The Way You Look Tonight" so I counted both seperately. (SATWYLT wasn't the single, so it peaked #46 on Airplay)
*2Pac's #1 was credited as "How Do U Want It/California Love" so I counted each individually. (California Love wasn't the single, so it never charted on Airplay)
*Toni Braxton's #1 was credited as "You're Makin Me High/Let It Flow" so I counted each individually. (Let It Flow wasn't the single, so it never charted on Airplay)