I have only come across the selection in the recording of 100 Years of Peter Pan - but I'd be interested to hear if a complete recording exists.
There is a book with the complete score of the play by John Crook (including the song for Wendy's House) published in 1905 by Price & Reynolds - copies occasionally turn up on eBay. Or you might be able to consult a copy in a reference library? The book contains music to other plays and is called Peter Pan, Catch of the Season, Etc.
The first two bars of the music also appear in the text of The Peter Pan Picture Book and the Peter Pan Keepsake, both written by Daniel O'Connor and published 1906-07. The PP Picture Book is retold from the play, and is quite different from Barrie's own novelisation.