John, Ive been looking at this period too. First in relation to my family who came to Aus. from Cornwall in 1848, and also in researching an unrelated performer. Naturally, being a singer of old songs, it's the songs I've noticed.
I've read a lot of diaries kept by passengers. So far I've found mention of several popular songs of the period -- sung by either the sailors or the passengers, or both. I've not seen mention of a shanty -- as such -- or even a work song -- as such.
Is it only work songs that you are looking for?
Also is it just the run from San Francisco?
Has anyone suggested you look at family history sites? Often there are quite detailed accounts of voyages to Australia.
Good luck.
Cheers, Joy