Now that the Catholic registers are available, and indexed, have you tried searching?
Looking for an Edward Sinnott, son of Edward and Catherine, in the 1850s time frame, I see only one match
Name: Edward Sinnott
Baptism Age: 0
Event Type: Baptism
Birth Date: 1854
Baptism Date: 24 Jul 1854
Baptism Place: St Andrew's, Dublin city, Dublin, Ireland
Parish Variants: St. Andrew's, Westland Row, Westland Row
Diocese: Dublin
Father: Edward
Mother: Catherine
Searching for a brother James provides the following record for an older brother.
Name: James Sinnott
Baptism Age: 0
Event Type: Baptism
Birth Date: 1851
Baptism Date: 5 Oct 1851
Baptism Place: St Andrew's, Dublin city, Dublin, Ireland
Parish Variants: St. Andrew's, Westland Row, Westland Row
Diocese: Dublin
Father: Edward
Mother: Catherine
I think it is reasonably clear that these are a good match. James would be a tad young to enlist in 1864 (though, unfortunately, not unheard of), so I wonder if you ever established whether the James who joined up was related, or not.