There is a rapier in the Pilgrim Hall Museum, which is attributed to Myles Standish:
https://www.pilgrimhall.org/ce_arms_armor.htm
As from the description of an exhibition there (
https://www.pilgrimhall.org/pdf/Arms...f_Pilgrims.pdf),
one could speculate, this, less "fantastical" weapon was the "true" sword of M.S.
Perhaps it would be interesting to contact them directly about this matter/if the sword with inlays still is in their collection. They say, items presented on website are a selection.
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On the same site there is found the inventory of M.S.
https://www.pilgrimhall.org/pdf/Myle..._Inventory.pdf
and it says "It one sword one Cutles 3 belts", so there must have been a sword and a cutlass indeed.