Source: Secondary reference
According to some sources, dha shay is Burmese for the long curved sword of this culture.1
During extensive research in primary sources, including comprehensive period dictionaries, I have not been able to find the term, and I suspect it might be a neologism; A more recent term that was not used back in the 19th century.
For more information on the sword called da, see my glossary article: da (ဓား)
1. Robert Hales; Islamic and Oriental Arms and Armour: A Lifetime's Passion, Robert Hales C.I. Ltd., 2013. Pages 148-149. On this page, Hales quotes long time collector Noel Singer.