I’ve given up trying to figure out what band this was.
-Album was released sometime 1995-1997.
-Album cover was solid green background with a zebra standing there.
-Title was something like “So, you’d rather be…”
-They only had one hit and I know they performed it on Letterman.
-Song was hard driving guitars to the point of distortion while the lead singer sort of sang in a melancholy way.
???
I did some searching around because I was bored and I love 90’s music. I am beginning to think either you made this up, the album you’re thinking is a single, or you are crossing up facts 
I looked here to see all the David Letterman guests (seasons 2-5 will take you from 1995 to 1997) and didn’t come up with anything. I cross-referenced with Amazon to see album covers.
However, here’s a list of bands I am 99% sure that it is NOT - based on Amazon and general knowledge of albums of that timeframe.
If you figure it out on your own, post it here because I am dying to know now, too!
Bad Religion
Big Head Todd & The Monsters
Everclear
Pearl Jam
Tonic
Foo Fighters
Matchbox 20
Seven Mary Three
Silverchair
Collective Soul
Radish
Goo Goo Dolls
Blind Melon
Wilco
Verve Pipe
Matthew Sweet
James
The Heads
Midnight Oil
The Cicadas
311
Butthole Surfers
Paul Westerberg
Mighty Mighty Bosstones
Dave Matthews Band
Sponge
The Wallflowers
The Cure
Hootie & The Blowfish
Sonic Youth
Soul Asylum
Counting Crows
Dog.s Eye View
Del Amitri
Afghan Wigs
Cowboy Junkies
Spacehog
Toad the Wet Sprocket
Green Day
Spin Doctors
Pete Droge
Hothouse Flowers
Crashtest Dummies
The Jayhawks
Whiskeytown
Bush
Cake
Oasis
The Offspring
Radiohead
The Flaming Lips
Belly
Bela Fleck
Blues Traveller
Evan Dando
The Lemonheads
Better Than Ezra
The Rembrandts
Primus
REM
Phish
White Zombie
Sugar Ray
Smashmouth
Days of the New
Chumbawumba
Jars of Clay
It’s Hum, You’d Prefer an Astronaut. I love that album.
ETA: Their one hit was “Stars.” The single was a pared-down version of the song and, IMHO, not as good as the full version. I’d also like to add that I am very excited to 1) know the answer and 2) be the first person to reply with the answer. That’s never happened here before. 
Lloyd Cole had minor airplay in mid 1990’s with “So You’d Like to Save the World” off the Bad Vibes LP- no zebra on the cover though.
That’s It!!
I knew the title was something like “You’d rather be an astronaut” but “You’d Prefer an Astronaut” is correct.
I knew Hum was on Letterman at sometime or another. Maybe it was Conan?
Complimentary video
The followup record, downward is heavenward, is still revered as a classic among many.