Hi kk
Think I'd go wth the Church record - I've seen quite a few errors on dates of marriage on the Scottish birth certs - some have different places and dates with each child
I've been working around Patrick's family as I can't see anything before his marriage to Mary.
The witnesses on his marriage to Ann were John Sherry and Catherine O'Brien/Brian. They are married* and, on the 1881, John was born Co Monaghan (circa 1827 -varies between censuses) and Catherine was born Edinburgh. They were already married and living Cowgate in 1841.
Maybe there wasn't any family connection but it might be worth checking on them.
Wonder if Patrick had any siblings?
I couldn't find a death in Scotland

Gadget
* confirmed by son's birth record.