Hello Robert, yes, I can give you a list of his ships, or rather the order in which he served on them, no problem:-
5th Feb 1867 - 8th Feb 1868: EJ served as 'Boy' aboard his half brother's ship, Senator Weber.
9th Feb 1868 - 3rd Sept 1870: Served as 3rd mate aboard Senator Weber
18th Oct 1870 - 6th March 1871: Able Seaman aboard the Amoy.
24th March - 15th July 1871: Able Seaman aboard Madge Wildfire.
24th Aug 1871 - 19th Jan 1872: 2nd mate aboard Record.
28th Feb - 27th July 1872: 2nd mate aboard the Agra.
27th Sept 1872 - 3rd March 1873: 2nd mate aboard the Quebec registered N. Mosher.
15th July 1873 - 4th May 1875: Served three terms as mate aboard the Liverpool registered Arzilla.
May 1876 - Jan 1880: Smith's first command, the 1040 ton Liverpool registered ship Lizzie Fennell.
March 1880 - March 1882: Smith served as fourth and later third officer aboard the White Star S.S. Celtic.
March 1882 - March 1884: Second officer aboard the S.S. Coptic in the Pacific service.
March 1884 - July 1885: second officer aboard the S.S. Britannic.
July 1885 - April 1887: first officer aboard the S.S. Republic.
April - August 1887: Temporary command of S.S. Republic.
August 1887 - February 1888: first officer aboard S.S. Britannic.
April - May 1888: Commanded S.S. Baltic.
June - September 1888: Commanded S.S. Britannic.
December 1888: Command of the cattle transporter S.S. Cufic for her maiden voyage.
January 1889: Command of S.S. Republic.
April - July 1889: Commanded S.S. Celtic.
December 1889 - February 1890: Commanded S.S. Coptic in the Australian service.
December 1890 - February 1891: Back to the North Atlantic as commander of S.S. Adriatic.
March - April 1891: Commanded S.S. Runic.
May 1891 - May 1893: Commanded S.S. Britannic.
June 1893: Briefly in command of S.S. Adriatic.
July 1893 - January 1895: Commanded S.S. Britannic.
January 1895: Briefly back in command of S.S. Cufic.
January - April 1895: Commanded S.S. Britannic.
May - June 1895: Commanded S.S. Germanic.
July 1895 - November 1902: Smith's longest command, the S.S. Majestic, including two trips to South Africa, transporting troops to the Boer War.
December 1902 - May 1903: Commanded S.S. Germanic, while Majestic was refitting.
May 1903 - June 1904: Again commanded S.S. Majestic.
29th June 1904 - March 1907: Commanded the new R.M.S. Baltic.
8th May 1907 - February 1911: Commanded the new R.M.S. Adriatic.
May 1911 - March 1912: Commanded the new R.M.S.
Olympic.
April 1912: Commanded R.M.S. Titanic.
The majority of these details come from Smith's own service records held at the National Maritime Museum in London. How accurate they are, I cannot say, the actual logs of particular ships may vary the dates. Anyhow, I hope they're of help.