I am not sure that the premise of this topic is absolutely correct because I think a basic of appealing to a younger audience is that you have to change the rhythm to something more familiar. When you drop 'swing' from the format, it then becomes debatable as to whether you are still playing jazz.

For instance, perhaps the most successful big band we ever had in Australia was the Daly Wilson Big Band. Warren Daly was fond of saying something like, "We are not a 'swing' band. We are a big 'rock 'n roll' band!" That always made me smile because they had some of the best jazz musicians in the world in that band (James Morrison etc.) and it could swing like crazy when it wanted to. Ed Wilson is these days perhaps Australia's most successful arranger and his charts are played by all the youngsters in their High School big bands, jazz bands and stage bands. This is one of the original Daly Wilson Big Band Charts but played by a young band:

https://www.youtube.com/watch?v=ZDDOUohc518

Is it jazz? I confess I sometimes have doubts but I love it nonetheless! We certainly have to interest the younger musicians if jazz is to survive.

And so I have personally used Band-in-a-Box to explore a lot of ways of playing tunes other than jazz standards, but still retaining the basic elements of jazz. One of the easiest ways is to play Smooth jazz, but a diet of music all played in that style bores me to tears. Great for sitting in a coffee shop or restaurant but for real jazz improvisation and excitement for a live audience, perhaps not. It is a dilemma for we jazz fans and musicians.

Anyway, that is enough soapboxing. Here is my list of suggestions:

Ain't No Sunshine by Bill Withers
The Air That I Breath by Albert Hammond & Mike Hazlewood
Always On My Mind by Thompson, James & Christopher
And I Love Her by Lennon and McCartney
And I Love You So by Don McClean
As Tears Go by Mick Jagger, Keith Riohard & Andrew Oldham
Better Be Home Soon by Neil Finn
Candle In The Wind by Bernie Taupin & Elton John
Can You Read My Mind by John Williams and Leslie Bricusse
Colour My World by James Pankow
Crazy by Willie Nelson
Crying by Roy Orbison & Bill Dees
Don't Cry Out Loud by Peter Allen & Carole Bayer Sager
Don't Know Why by Jesse Harris
Don't Let Me Be Lonely Tonight by James Taylor
Don't Let The Sun Catch You Crying by Gerard Marsden, Les Chadwick & Les Maguire
Endless Love by Lionel Richie
Every Breath You Take by Sting
Every Time You Go Away by Daryl Hall
Have I Told You Lately by Van Morrison
He Ain't Heavy.. He's My Brother by Bobby Scott and Bob Russell
Hello by Lionel Richie
How Can You Mend A Broken Heart by Barry & Robin Gibb
How Deep Is Your Love by Barry, Robin & Maurice Gibb
I Don't Know How To Love Him by Andrew Lloyd Webber & Tim Rice
I'd Rather by Sorry by Kris Kristofferson
If by David Gates
If I Fell by Lennon & McCartney
If Tomorrow Never Comes by Kent Blazy & Garth Brooks
If You Leave Me Now by Peter Cetera
I'll Stand By You by Chrissie Hynde, Tom Kelly & Billy Steinberg
Imagine by John Lennon
In Dreams by Roy Orbison
In My Life by Lennon & McCartney
Just The Way You Are by Billy Joel
The Long And Winding Road by Lennon and McCartney
Long, Long Time by Gary B. White
Love Has No Pride by Eric Kaz & Libby Titus
My Love by Paul & Linda McCartney
On And On by Stephen Bishop
Please Don't Ask Me by Graham George Goble
She's Out Of My Life by Tom Bahler
Softly, As I Leave You by Hal Shaper & A. De Vita
Sweet, Sweet Love by Russell Morris
Tears In Heaven by Eric Clapton & Will Jennings
Through The Eyes Of Love by Marvin Hamlish & Carole Bayer Sager
True Love Ways by Norman Petty & Buddy Holly
Vincent by Don McLean
We're All Alone by Boz Scaggs
What I Did For Love by Marvin Hamlisch & Eward Kleban
While My Guitar Gently Weeps by George Harrison
Woman by John Lennon
Wonderful Tonight by Eric Clapton
Words by Gibbs Bros
World Without Love by Paul McCartney
You Are So Beautiful by Billy Preston & Bruce Fisher
You Are The Sunshine Of My Life by Stevie Wonder
You're The Inspiration by Peter Cetera & David Foster
You Needed Me by Randy Goodrum
You Raise Me Up by Rolf Lovland & Brendan Graham

Of course my taste in pop music might be a bit dated.

I also find that tunes played with a Latin rhythm (Bossa Nova, etc) tend to be liked by both old jazz fans and younger general audiences.

Then there is Funk and Ska with elements of pop and jazz built in.

Grah Jive Talk
"Don't worry baby, they'll swing their arses off."