This is pure speculation, but if your Wastie ancestors did live in Ireland, then there's a Scottish/Irish/Manx surname which might conceivably have been heard by English speakers as something like "Wastie". In Scotland and on the Isle of Man, the name was spelled Mac Uisdin, and in Ireland it was spelled Mac Úistin. According to MacLysaght in his Surnams of Ireland, both were branches of the Scottish Clan MacDonald (people from a number of Scottish clans migrated to Ireland in the Middle Ages, even before the Plantation of Ulster in the 17th Century). The name was apparently based on a form of the given name Hugh, and was anglicized in a number of ways, including MacCutcheon, Hutchinson, Hutchin, Kitchen, Houston, MacQuestion, MacQuiston, MacWhisten, and Whiston. I'm thinking that the last of those might conceivably be the source of your Wastie version of the name, because the final "n" would not have been pronounced very prominently in Irish (almost swallowed, in fact), and final vowel sounds were often heard yy non-Irish speakers as an "ee" sound. The name was obviously a hard one for English speakers to hear clearly. As I said, though, this is just speculation.