That 1904 emigration you found (rather than when Joseph was a teenager) is looking right.

In the 1901 census I think he was on the 'Nymph' No.57, in the Peel Fishing Fleet. Joseph Moore, S[ingle], aged 18, Residence Glenmay?, Patrick, born Patrick. The Master of the Nymph was Henry Watterson, and there were 5 other members of the crew - mostly young, between 18 and 30, with William Watterson aged 70 (Henry's father?).

Sue