That is definitely for the brides’ maids.
Dixie Chicken still kicks your third rate rhythmic butt.
Semi Charmed Life - forgot who sings it
Closer - Nine Inch Nails
In addition to all the songs with the “anti love and marriage” themes, you should play a few that would just be plain odd to hear at a wedding.
I suggest:
The Canadian National Anthem
Feliz Navidad
It’s Not Easy Being Green (Kermit the Frog)
Danny Boy
We Are The World
Quite a few songs by Squeeze would liven up the reception, including Up The Junction:
I never thought it would happen
With me and the girl from Clapham
Other possibilities include “Take Me I’m Yours”, “Separate Beds”, “Slaughtered, Gutted and Heartbroken” and of course “She Doesn’t Have To Shave”.
I was as a wedding where the dj called the happy couple for their 1st dance only to announce that they’d asked for ‘Unchained Melody’ by the Righteous Brothers, but he didn’t have that “so here’s ‘You’ve Lost That Loving Feeling’ instead” !
MiM
Some friends of mine used Percy Sledge’s When A Man Loves A Woman for their first dance.
You reminded me of another good one - Panic! At The Disco - I Write Sins, Not Tragedies.
"What a beautiful wedding!”, says a bridesmaid to a waiter
“And yes, but what a shame, what a shame
The poor groom’s bride is a whore”
Third Eye Blind.
“In the Pines” the Nirvana version (MTV Unplugged) if you can get it, otherwise the Carter Family recording.
Asleep by The Smiths. Because there’s no better way to celebrate the start of a new life together than with a song about suicide.
Hayley Westenra—“Bridal Ballad”…lyrics taken from Edgar Allan Poe’s “Bridal Ballad.”
Subtle AND pretty! 
Tina Turner - What’s Love Got To Do With It?
Hair of the Dog—Nazareth
Crazy Bitch—Buckcherry
REM - it’s the end of the world as we know it
AC/DC - highway to hell
Elton John - Funeral for a Friend / Loves Lies Bleeding
And, just for the record, two of my dear friends had a Muppets themed wedding.
Yes, they are both adults.
Yes, they danced to It’s Not Easy Being Green.
As it should so happen, puppeting is right in my wheelhouse and I’m definitely considering using them.
That one is brilliant.
The Imperial March from the Star Wars OST / John Williams for the procession. Make sure you both keep entirely straight faces.
My best friend had Supertramp’s “Take the Long Way Home” played in the mix tape at their reception. I pointed out that this wasn’t quite the perfect picture of marital felicity, but she said she just likes the song.
I sang this in a karaoke at my little sister’s bachelorette party the night before her wedding.
What?! Nobody has mentioned One Week by the Barenaked Ladies?! The iconic lighthearted song about a lovers’ spat? As a plus, it will get people dancing.
Led Zeppelin - Dazed and Confused
Gloria Gaynor - I will survive
Gillette - Short Dick Man