In the 1901 census there is a Stewart Wetherall living with James who is 4 years older.Given that people seem to guess at their age, this might be your William James and Stewart.
However there is a William John Wetherall living quite nearby Church of Ireland 66 clerkb. Armagh with wife Ann Jane 69 and son Alfred 29, a clerk b. Armagh.I would have expected his name to be in your family if this were your Stewart.
The only other Wetherall I have seen so far in the census is Margaret 49 years who probably lives much much farther away.One of her daughters married a McKinley.
"98James Wetherall COI 72laborer widow b. Armaghdaughter Mary Jane 29 seamstress b. Armagh Stewart Wetherall boarding68 general laborermarried b. Armagh"