The first edition was a limited run of 55 copies on handmade paper (Victor Gollancz: London, 1929; pp 85). Unless that edition contains material not in the 1930 edition, you're stuck, probably. I take it that Maclaren didn't specify tunes? Not having seen the book, I can't really be of any help (I'm a lot less knowledgeable than Bob suggests!) but I shouldn't be surprised if this were a literary work not really intended for performance. Maclaren may well have modelled his verses on existing songs that he knew, of course, but any identification is likely to be guesswork unless his daughter can help with inside info.

In cases where a score is available separately from the libretto, you'd expect some reference to it; the British Library online catalogue (admittedly not complete) lists only the three books by Maclaren. You could try contacting a dealer who has the original limited edition in stock, just to check, but I wouldn't hold out much hope.

Meanwhile, here is a photo of a sailor with a banjo:  Sailor with Banjo (c.1890?)

There is some related genealogical information at  Maclaren genealogies