If you were very lucky and did manage to find a Free Church or other non-C of S register with your people in it, that would be the closest you would ever get to proof.
Apart from the parish or other church registers, the only place you are likely to find an indication of what denomination they belonged to is by looking to see what type of marriage ceremony family members undertook after 1855, especially the daughters, as it was customary for a marriage ceremony to be held in the bride's home and conducted by the family minister. So if the majority of daughters of a particular family were married by (a) Free Church minister(s), it would be reasonable to suppose that the family belonged to the Free Church.
Dunnichen Parish Kirk was the Church of Scotland. Free churches didn't necessarily have a separate graveyard. Being buried in a parish kirkyard does not mean they were members of the C of S.