I've combined a reconstructed melody line, from Chas. Z. Rockwell's instrumental parts (transposed from A-flat to F), with the Carter's triple meter and bits of their tune (particularly at the "Too late" part). I also made some other tweaks, particularly to the ends of both the verse and chorus. Here is the result:

X:1
T:One Little Word
C:Words and music by Gussie Lord Davis, 1896, pub. 1899
Z:Artful Codger, 2008
M:6/8
Q:1/8=160
L:1/8
K:F
% Verse
C| A2 F B2 A | G D2-D z D | E2 E F2 G | C3-C z C |
D2 D E2 F | F C2-C z A | A2 G G2 D | G3-G z C |
A2 F B2 A | G D2-D z E | G2 G F2 E | A3-A z A |
c2 c B2 A | =B B2-B z B | c2 G GFD | G3-G2 z ||
% Chorus
A2 ^G/A/ F2 E/F/ | A2 G ^F2 G | D3-D2 z | B2 ^F/A/ G2 E/D/ |
D2 C CEB | A3-A2 z | A3 F2 z | A3 F2 z | [M:9/8] G2 A c B2 A2 B |
[M:6/8] D3-D2 z | F2 G/F/ A2 F | E2 A G/ (G2 F/) | F3-F z2 |]