The William Stetson was chartered by the church to carry return missionaries and converts from Liverpool, England to New York. They left Liverpool on 26 April, 1855 and arrived at Castle Gardens in New York 27 May, 1855.
Records of the journey can be found in the Mormon Immigration Index. The following information is from that index.
On the twenty-sixth of April, 1855, the ship William Stetson cleared from the port of Liverpool, and sailed for New York with two hundred and ninety-three Saints on board, under the presidency of Elders Aaron Smethust, Francis Sproul and William Wright. This was the last company of Saints forwarded under the American Emigration Law, and swelled the number of emigrants sent out by the presidency in Liverpool since November, 1854, to three thousand six hundred and twenty-six, of whom one thousand one hundred and twenty-seven came out by the Perpetual Emigration Fund. It is estimated that about one thousand five hundred of them reached the Valley in 1855, while the remainder located temporarily in various parts of the United States in order to obtain means to complete their journey to Utah whenever circumstances would permit.
The nationality of the emigrant was as follows: English, 2218; Scotch, 401; Welsh, 287; Irish, 28; from France Channel Islands, 75; Danes, 409; Swedes, 71; Norwegians, 53; Swiss, 15; Italians 15; Germans, 13; Prussian, 1. The William Stetson had a fair voyage across the Atlantic, and arrived at New York on the twenty-seventh of May. Two births and four deaths occurred on board.
The following image shows a portion of the passenger list for the William Stetson for the journey.
Passenger # 97 is William Wilkes from Tewkesbury, England.
This image shows William Wilkes as a member of the Mormon group on the ship