I saw on the Foundation Church of Ireland Shankill but wasn't sure enough to give you the information as a fact.
Shankill Parish baptism records exist from 1817-1927 but they have no marriage records.
Latter Day Saints:
I have a CD with marriages for Belfast, Church of Ireland, it doesn't say St. Anne's or Shankill.
No marriages for James & Julieanne Stewart
These other Belfast marriages 1847-1862 all have different father's names so more than one Drummond family
again no St. Anne's or Shankill by name.
Fathers: Robert Drummond, John Drummond, James Drummond
I also checked ALL Ireland not just Antrim with both names
but no matches. Perhaps Elwyn knows why the Church of Ireland had registrations of marriages from 1845 and did all Parish's do that? I know the RC started 1864+
If you want the details let me know.
The Church of Ireland Representative Library website www.library.ireland.anglican.org
states that records from Northern Ireland parish which are not retained in local custody are held at the Public Records Office: PRONI
However, the Representative Library do have baptisms for St. Mary's, Belfast from 1867 to 1957 as well as marriages and deaths. Not that those will do you any good and you need to
do in person research.