Lyrics and chords copied from http://kristinhall.org/songbook/USFolk/WednesdayNightWaltz.html:


WEDNESDAY NIGHT WALTZ*

G             Gdim G            Gdim G          Gdim            G Fdim
Sweetheart of mine, sweetheart divine, come have a last waltz with me.
Am         D   G          Em          A7             D7
I love you so; want you to know you're mine 'til eternity.
G#dim       Am      D7                   G         Em            D7
We'll dance the whole waltz through while I whisper love words to you.

CHORUS:
      G          D7       G    G7    C         F#7   G
Let's dance while they are playing the Wednesday Night Waltz.
               D7      G         A7             D7
Let's join the couples swaying before the music halts.
      G    D7         G       G7 C       F#7         G    G7
Close to my heart I'll press you to prove my love is not false.
    C          F#7 G       E7    A7       D7    G
Sweetheart, let me caress you to the Wednesday Night Waltz.

I knew that you would love me, too; I saw it deep in your eyes.
Now I'm complete; you are so sweet; you're just a wonderful prize.
I love to hold you near and hear you say, "I love you, dear."

CHORUS: [new words]
I love a tune so mellow the Wednesday Night Waltz.
And when I hear the cello, my very soul exalts.
With music so entrancing, I'll never find any faults.
    C          F#7    G       E7    A7       D7    G
Sweetheart, when we are dancing to the Wednesday Night Waltz.

[*According to WorldCat.org, 3 university libraries have copies of sheet music titled WEDNESDAY NIGHT WALTZ, and they credit Spencer Williams as songwriter (New York City: Triangle Music Pub. Co., 1928)—but without seeing the sheet music, I can't verify that it's the right song. BMI.com has 12 listings for the same title, each with different writers. I can't tell whether these are different songs with the same title, or different lyrics to the same tune, or conflicting claims to the same song, or—?

[78discography.com lists the following early recordings:

Leake County Revelers, 1927
Kessinger Bros, 1928
North Carolina Hawaiians, 1928
Bar Harbor Society Orch, 1929
Bud & Joe Billings, 1929
Cruther Bros, 1929
Frank Luther & C. Robison, 1929
Harry Pomar Hotel Ansley Orch, 1929
Walter Kolomoku's Hawaiians, 1929
Carter's Orch, 1930
Fiddlin' Doc Roberts Trio, 1931
Riley Puckett, 1934
Stripling Brothers, 1934
Shelton Brothers, 1938
Wiley Walker & Gene Sullivan, 1940
Cope Brothers, 1947
Elmer Christian Bar-X Cowboys, 1947
Jack Youngblood, 1953]