One possibility worth exploring is that Captain Sparrell took to seafaring in England and that he made his way to America as crew (or even as a master). If that is the case, then there may be some records of him in a collection held at the UK National Archives at Kew.
There is a class of records called Merchant shipping: crew lists and agreements 1747-1860. A guide to these records called Domestic Records Information 92 is available at https://www.nationalarchives.gov.uk/documents/research-guides/merchant-shipping-crewlists-agreements-1747-1860.pdf. Note however that most of these lists assume you know the likely port from which he sailed. So you may have a long search ahead.
If you knew he was a ship's master in England then The Registry of Shipping, later renamed Lloyd’s Register, could possibly include him. But its first issue was printed in 1764 by which time James was probably across the Atlantic. However, if all else fails you can find most of these in Google Book Search.