If you mean William Dunbar, I don't see how O Cathain could have been even "on the edge of his circle," since Dunbar died around 1520 and "Give Me Your Hand" is said to have been composed more than a century later.

Macaronic or hybrid verse like Dunbar's appears to have originated on the Continent in the 12th century. The paradigm macaronic poem consists of alternating lines written in each language.

But I think you know that. I don't know if any surviving work combines Latin and Gaelic. In any case, the Scots could easily have imported the macaronic style from the Continent and adopted it, not to show off their level of sophistication, but because it was a novel and interesting style well suited to the writing of Christian poetry.