Did a bit more digging which is confirming my suspicions. Firstly, I got Hugh Orr's 1869 detail registration (PM me with an email address if you'd like a copy).
Hugh Orr died in Ballymoney Workhouse (unfortunately usual or former address not listed), married, labourer, cancer of kidney (1 yr.), informant is not a relative as I'd hoped.
Now, starting with the 1845 marriage certificate -
1) James' residence is Scalty which isn't far from Rhee. This is where he was living at the time of the marriage but it's unlikely he was born there. It's more likely that he came into the area to work and met Jane Shirley. I think he was from Co. Antrim or more exactly probably from Finvoy or vicinity. More on this in a moment.
2) James' father is listed as Hugh Orr, a miller. There is no indication of any such miller in the Aghadowey area with this name (and there was no mill in Scalty). I think he was a labourer, perhaps a weaver, but not a miller.
I should note that Jane Shirley's uncle, Valentine Shirley, married Ann Orr (daughter of Paul Orr & Isabelle Boyd) but I can find no connection between James Orr and Paul Orr. I have, however, found quite a few possible connections to James Orr in the Ballymoney area (remember this is where James & Jane Orr lived before moving to Scotland). It's unfortunate that most of their children were born before birth registration started in Ireland so we can't yet be sure where they lived before 1864. The baptismal register for Aghadowey Presbyterian Church (the Shirley's church) starts 1855 and doesn't record any of the children (another reason I think they were in County Antrim pre-1864).
I'm still trying to find Hugh Orr's wife (death registration says married) and a few other bits before posting everything.