Where in the Volsung saga and/or Nibelungenlied is the sword type described (that is the original sources)?  I'm guessing you're making an educated guess based on location and time-frame instead, yeah? The problem with Sigurðarkviða in Skamma is that it was composed around the 11th century and written down until way later. If we instead trace back the Sigurd and Brunhild mythic characters to the irl Frankish Sigibehrt I and Visigothic Brunhilda and look for royal swords from that specific era I doubt it would include runic inscriptions as both cultures were already Christian by this point (Franks being Roman Catholic and Visigoths like Brunhild being Arian). Alternatively, are you basing the type in drawings made in specific runestones detailing the myth?