Have you tried looking at St Joseph's Catholic cemetery in Airdrie? It would have been closer to Holytown than Dalbeth, it opened about 1860 and the records are with North Lanarkshire Council.
Holytown cemetery didn't exist in 1881 but it is possible that your ancestor was interred in the churchyard there in 1881. As far as I know, no records exist for the churchyard before 1912.
Wrangholm has records from about 1876 but the chance of Roman Catholics being interred there are slim, it wasn't within the mainstream Church of Scotland and only church members and their families would have been allowed to use the burial ground. Holytown, (about a mile along the road from Wrangholm), was made a Quoad Sacra parish in the 1860s and anyone living within its boundaries, no matter of what religion, would have had the right to be interred in its burial ground.