I've heard one or more tunes (not songs) with the tiltle 'An Súisín Bán' played and they didn't resemble the usual air for Casadh an tSúgáin.

There's a simple setting of a hornpipe called "An Súisín Bán" published in Eithne and Brian Vallely, "Learn to Play the Fiddle with Armagh Piper's Club"

By the way, Áine, the tune for "Dóchas Linn Naomh Pádraig" is in the same publication.