The family of Shaws in the Highlands is of Mackintosh origin, just as are the Farquharsons, MacThomases and MacRitchies. The chief of the Highland Shaws is actually chief of Clan Ay, the second tribe of Shaws after Rothiemurchus. Not all of the name Shaw are Highland. There are actually many, many more Shaws of Lowland and English origin. You don't say where your Shaw grandfather lived in America or where (if) in Scotland he originated. Either bit of information will more accurately place that branch of your family in Scotland.