I doubt Stuart Boyd is Charles. Stuart may be after mother Mary Stewart.
You are trying to trace people across the famine and even if Charles survived eg Canada didn't really keep immigration records until 1865 and US census would just have him as Charles from Ireland.
The 1846 entry #257 with no forname could be WJC or anyone, no indication even of gender. No entries for 1840 or 1841 and a gap in 1844, may be more omissions on microfilm images not so obvious. It would be unusual for there not to be 6-10 children so some may have been baptised before or after the Presbyterian transcript or elsewhere.
My own tree has initial children late 1820's baptised 1st Lurgan Presby then seem to swap to Lurgan C of I 1830's with re-marriage there 1853. He left a 2 page will naming most children including married daughters so know not two different Hectors & families. Charles had only 4 acres on Griffiths and may have moved a few miles locally for work & church at times.
No records were kept of people travelling from Ireland to or from G.B. would be equally accurate both then and now.
I was about to say he doesn't seem to be on the 1871 census from trees and married 1875 but he was, as Stewart B, aged 26 (1845) lodging 4 Dover Street, Chorlton upon Medlock, Lancashire (Manchester) same area as 1881. Found on Findmypast - Ancestry had him transcribed as Hewitt
https://www.ancestry.co.uk/search/collections/7619/records/5045499 FindMyPast's census image is better.
