That song has already been posted in a previous discussion: White, orange and green. A little ironic, perhaps, to use a piece of music which is all about reconciliation, for a song which is anything but that; mind you, it's better-written than the Wolfe Tones' effort! I tend to think it wisest to leave well alone, and resist the temptation to set one's own words to instrumental pieces like this unless they are of equal quality; which is pretty rare.

A number of largely apocryphal stories have circulated about the circumstances of the tune's composition; further details can be seen at Andrew Kuntz's The Fiddler's Companion:

Give Me Your Hand (search results).

The Gaelic and English titles seem not to have appeared in print until 1840; prior to that (at least since 1644) the piece was known by its (original?) Latin name, Da Mihi Manum. Ruari Dall wasn't exactly "on a visit" to Scotland; he lived there for most of his life, and the tune was first published there.