Here's the list, probably not complete and some odd choices. I picked the songs which have at least a version that is listenable.
It's up to you to start eliminating.
Anna (Go To Him)
Chains
Boys
Baby It’s You
A Taste Of Honey
Twist And Shout
Till There Was You
Please Mr Postman
Roll Over Beethoven
You Really Got A Hold On Me
Devil In Her Heart
Money (That’s What I Want)
Rock And Roll Music
Mr Moonlight
Kansas City/Hey Hey Hey Hey
Words Of Love
Honey Don’t
Everybody’s Trying To Be My Baby
Act Naturally
Dizzy Miss Lizzy
Long Tall Sally
Slow Down
Bad Boy
Matchbox
I Got A Woman
Too Much Monkey Business
Keep Your Hands Off My Baby
Youngblood
A Shot Of Rhythm And Blues
Sure To Fall
Some Other Guy
That’s Alright Mama
Carol
Soldier Of Love
Clarabella
I’m Gonna Sit Right Down And Cry Over You
Crying Waiting Hoping
To Know Her Is To Love Her
The Honeymoon Song
Memphis Tennessee
Lucille
Lonesome Tears In My Eyes
Hippy Hippy Shake
I Just Don’t Understand
So How Come (No One Loves Me)
I Forgot To Remember To Forget
I Got To Find My Baby
Oh My Soul
Don’t Ever Change
My Bonnie
Three Cool Cats
Searchin’
Sheik Of Araby
Besame Mucho
How Do You Do It
Lend Me Your Comb
Leave My Kitten Alone
Ain’t She Sweet
Medley: Rip It Up/Shake Rattle And Roll/Blue Suede Shoes