Webster says the mor makes it "great sword", which might well indicate the two handed, but also goes on to say that both usages are correct.
It does indicate the basket hilt would be the double edged version. Single would be the backsword. Webster also notes the earliest usage as
1527. The large two handed with quatrefoil tips, IIRC, is a copy of an extant gallowglass sword, or extant drawing of the sword, and the gallowglass
troops go back into the late 1200s. So, which is the chicken, which the egg?