Any chance this might be Arthur in the 1881 census?
Name: Arthur Butler
Age: 18
Estimated Birth Year: abt 1863
Gender: Male
Where born: Liverpool, Lancashire, England
Civil parish: Vessels
County/Island: Yorkshire
"Romes Or Romeo"
Occupation: Third Hand (FM)
Registration district: Hull
Sub-registration district: Myton

There is an Arthur Butler living in Sculcoates in the 1901 census, listed as a 'navvy' and born 1863 Hull, Yorkshire, living with daughter Ruth b 1894 Hull.

I did find Joseph again in 1891 and 1901. In 1901, he is a night watchman at the port, living in Sculcoates with his daughter-in-law Ette, born 1861 Hull, listed as married and a charwoman, and her children:
Archibald b 1891 Hull, Violet b 1893 Scotland, and Joseph born 1895 Scotland.