You can't really cheat on the C chord if you want it to sound like Ed.  He plays 
around with his index finger on the C chord to get the sound that he does.

Ed Plays it in capo 3

Chords used : Em , G , C , D

[Ed ]
        Em
I said hush little baby
              C
Don't you cry
        G
I said hush little baby
Don't you cry , No
        Em
I said hush little baby
              C
Don't you cry
        G
I said hush little baby
Don't you cry , No

[Wretch 32]
            Em
I'm saying hush little baby
Don't you cry
C
Daddy ain't sure he can raise you right
G
I ain't even good with saving my money
Why should I think I could save your life
Em
The whole family's gonna think I'm a devil
C
Cos I don't want to see my angels eyes
G
I say this with one hand on my heart
Guilt ain't gonna make me change my mind
Em
My first thoughts were my worst thoughts
C
Running through my head in circles
G
The world's gonna hate me for saying this
But patience is a virtue
C
So we don't have to rush
For our first yute
C
We could take time do rehearsals
D
And I ain't acting, this is personal
And I ain't doing this just to hurt you

[Chorus]
Em                               C
I should say goodbye before I say hello
            G                           D/F#
So darling hold me closely tonight
            Em                            C
Cause' if you open your eyes I'll never let you go
        G                                    D/F#
Moving slowly we'll both sleep tonight
              C                 
And I'll be dreaming till you wake me up

[Wretch 32]
Em
When I'm telling her about raving
C
She's telling me about cravings
G
I just want her to get the message
I don't want to have to be so blatant
Em
So I told her my life ain't balanced yeah
C
So the time ain't right
G
She said God's clocks the only one that matters
And it's about time I tried
Em
And if I listen to my family
C
Then I'll be a new addition to my family
G
I can't help feeling peer pressured
Everyone's looking down but
They don't understand me
C
And everyone's so suggestive
C
I'm getting mixed messages
But nobody's rang me huh
D
I ain't saying this is a game
But when I say the wrong thing
Everybody wants to hang me

[Chorus]
Em                               C
I should say goodbye before I say hello
            G                           D/F#
So darling hold me closely tonight
            Em                            C
Cause' if you open your eyes I'll never let you go
        G                                    D/F#
Moving slowly we'll both sleep tonight
              C                 
And I'll be dreaming till you wake me up
[Ed]
 Em
Hush little baby
Don't you cry
        C
I said hush little baby
Don't you cry , No
        G
I said hush little baby
Don't you cry
        D/F#
I said hush little baby
Don't you cry , No

[Chorus:]
Em                               C
I should say goodbye before I say hello
            G                           D/F#
So darling hold me closely tonight
            Em                            C
Cause' if you open your eyes I'll never let you go
        G                                    D/F#
Moving slowly we'll both sleep tonight
Em                            C
I should say goodbye before I say hello
            G                           D/F#
So darling hold me closely tonight
              C [one strum]
And I'll be dreaming till you wake me up

Enjoy!