Who originally recorded the song 'If you don't want my peaches then stop shaking my tree' (or something like that)?

“IF YOU DON’T WANT MY PEACHES”
by Irving Berlin was published 9 May 1914.

'If you don't want my peaches, you'd better stop shaking my tree' was written by Irving Berlin but the song was either unpublished or unsung during his lifetime. After his death, it was published by the Irving Berlin Music Company as part of the 'Lower East Side Songbook'. A two-CD album entitled 'Unsung Irving Berlin' was issued a few years ago. On this, 'Peaches' is sung by Mary Ellin Lerner, Berlin's granddaughter.

https://grahamsdownunderthoughts.blogspot.com/2011/06/if-you-dont-want-my-peaches-irving.html

I'm only suggesting this because the other seems rather obscure. The Steve Miller Band did a song called The Joker in 1973 which included this lyric:

You're the cutest thing that I ever did see
I really love your peaches, wanna shake your tree

Here's an URL to the entire song:
https://www.songfacts.com/lyrics/steve-miller-band/the-joker

I have compilation CD of Bessie Smith numbers.

'Mamma's got the Blues' by Clarence Williams and S Martin was first recorded by Bessie, accompanied by Fletcher Henderson on piano, in New York on 28 April 1923. It contains the line: 'if you don't like my peaches thrn let my orchard be.' Masters of the single entendre those old blues singers!
There is just a possibility there may be a labelling/titling problem though. The first line of the song is 'Some people say the weary blues ain't bad' and although it doesn't sound like the versions of 'Weary Blues' that I can recall, it may be another version. Sorry to be inconclusive but I think I've reduced it to two possible songs.

I feel I should clarify my previous answer. The full title of the song sung by Mary Ellin Lerner on the CD mentioned is actually 'If You Don't Want My Peaches, You'd Better Stop Shaking My Tree'. It was for brevity's sake that I reduced the title to 'Peaches', but I realise now that this may have been confusing.

For the tune and lyrics, see: http://www.lyricsmania.com/if_you_dont_want_my_peaches_youd_better_stop_shaking_my_tree_lyrics_irving_berlin.html

I must admit that I don't recognise either the words or the tune of this song so it probably isn't the answer you are looking for, Jam Tomorrow. Good luck!