"Who's Gonna Shoe Your Pretty Little Feet" is generally considered to be a Southern folk song with lyrical roots in Child Ballad #76 (more specifically the "Lass of Loch Royal" variation)
In 1927 Carl Sandburg also noted the connection of "Who Will Shoe Your Pretty Little Foot" with "The Lass of Roch Royal". SEE: The American Songbag
"The Lass of Loch Royal" was already published in "The Book of Scottish Ballads" (1845)
But even before that it was published in "The Minstrelsy of the Scottish Border" (1829)
But the earliest publication I found is in Robert Jamieson's "Popular Ballads and Songs"(1806)
The Bodleian Library also consists of a sheet with those "Who Will Shoe My Bonnie Feet" line.
But listening to various versions of "The Lass of Roch Royal" I think there's only a lyrical and no musical connection with the American traditional "Who Will Shoe Your Pretty Little Foot".
Peggy Seeger and Tom Paley sang both "The Lass of Loch Royal"and "Who's Going to Shoe Your Pretty Little Foot?" as title track of their 1964 Topic and Elektra album Who's Going to Shoe Your Pretty Little Foot?
Peggy Seeger noted on both versions: "Here is an excellent example of how a ballad contributes to (or becomes) a song, or how elements of a ballad may be isolated out to become independent pieces. "The Lass of Roch Royal" hardly exists in full form any more in the United States, the present text being a collation of two North Carolina versions. They are the only ones I have found in print that even suggest the full story. It could hardly be affirmed that the shorter, lyrical piece is actually a fragment of the longer traditional ballad, as the verses they hold in common have now become ‘floater’ verses to be found in at least a dozen other songs".
One of these other songs is "The Storms Are On The Ocean" sung by the Carter Family in 1928, which also contains the "Who Will Shoe Your Pretty Feet" lyric
The first recorded version of the American version of this traditional I found:
(o) McCartt Brothers and Patterson (1928) (as "Green Valley Waltz")
Recorded October 18, 1928 in Johnson City, TN
Released on Columbia 15454-D
Listen here:
The first recording to use the familar title "Who's Gonna Shoe Your Pretty Little Feet ?" is by the Renfro Valley Boys in 1932
(c) Renfro Valley Boys (1932) (as "Who's Gonna Shoe Your Pretty Little Feet ?")
Recorded December 1931 in Grafton, WI
Released on Paramount 3321 and Broadway 8334
Listen here:
(c) Monroe Brothers (1936) (as "Little Red Shoes")
Recorded: February 17, 1936 in Charlotte, North Carolina
Released on Bluebird 6645
Listen here:
(c) Hackberry Ramblers (1936) (as "Green Valley Waltz")
Recorded February 19, 1936 in New Orleans, LA.
Released on Bluebird B-2002
Listen here:
(c) Woody Guthrie & Cisco Houston (1945) (as "Who's Gonna Shoe Your Pretty Little Feet")
Woody Gutrie: lead vocal, guitar / Cisco Houston: harmony vocal
Recorded April 19, 1944
Matrix MA 27
Released as disc # 432-4 (part of the 4 disc album "American Folksay Ballads and Dances")
Or here:
(c) Wayne Raney (1947) (as "Green Valley Waltz")
Wayne Raney (Alton Delmore [rh gt], Rabon Delmore [tenor gt])
Recorded October 1946 in Nashville, TN
Released on King 676
Listen here:
(c) Patti Page (1951) (as "Who's Gonna Shoe My Pretty Little Feet")
Or here:
(c) Everly Brothers (1958) (as "Who's Gonna Shoe Your Pretty Little Feet")
Listen here:
(c) Kingston Trio (1960) (as "Who's Gonna Hold Her Hand")
Listen here:
As I said above in 1964 Peggy Seeger and Tom Paley recorded both "Who's Going To Shoe Your Pretty Little Foot" and its lyrical inspiration "The Lass of the Roch Royal".
(c) Peggy Seeger and Tom Paley (1964) (as "Who's Going To Shoe Your Pretty Little Foot")
(c) Peggy Seeger and Tom Paley (1964) (as "The Lass of the Roch Royal")
(c) Blue Sky Boys (1966) (as "Who's Gonna Shoe My Pretty Little Feet")
Recorded May 17, 1965 in Hollywood, CA
Blue Sky Boys (Bill Bolick, Earl Bolick + unknown musicians)
Listen here:
(c) Hootenanny Singers (1969) (as "Who's Gonna Hold Her Hand")
Listen here:
(c) Art Garfunkel (1997) (as "Who's Gonna Shoe My Pretty Little Feet")
Listen here:
(c) Billie Joe Armstrong + Norah Jones (2013) (as "Who's Gonna Shoe Your Pretty Little Feet")
"Foreverly" is a 2013 remake of The Everly Brother's album "Songs Our Daddy Taught Us" by Billie Joe Armstrong and Norah Jones.
Listen here:
More versions here:
The Carolina Tar Heels' "Who's Gonna Kiss Your Lips, Dear Darling" (1929) is sometimes considered a variant of "Green Valley Waltz"/"Who's Gonna Shoe Your Pretty Little Feet ?" but apart from the "Who's Gonna Kiss Your Lips" line, there is no textual and on the whole no musical similarity.
It's a variant of this traditional (SEE: Joop's Musical Flowers: Little Bunch Of Roses (1928) / Who's Gonna Kiss Your Lips, Dear Darling (1929) / Last Gold Dollar (1929) / Can't You Hear That Night Bird Crying (1936) / Rough And Rocky (1945) / Don't This Road Look Rough and Rocky (1954)
