If Mr Spitt was an American whaler, and you know the island the child was born on, there might be mention of an American whaling ship that went there at that period.
Find a copy of Where the Whalers Went, by Robert Langdon, which lists all the ports of call of American whalers in the Pacific, plus a few others.
It is available as a book from PAMBU at the Australian National University in Canberra, and in libraries. Once you have some possible ships, you can refer back to their logbooks, generally held in the museums along the eastern coast of northe America, but also available as microfilm from PAMBU.
There are also other books available about American whalers and their Pacific ports of call.