BTW, the sources I'm checking on are-
Small Arms of the Spanish Treasure Fleets, N. Wells
A Guide to the Artifacts of Colonial America, I. Hume
Artifacts of the Spanish Colonies of Florida and the Caribbean, Vol 2, K. Deagan
Hopefully, they may shed a little light?
Harold Peterson's 'Arms and Armor in Colonial America:1526-1783' is an excellent resource for weapons and shows both cup-hilts, hangers and smallswords recovered in the colonies. Being that the Jamestown settlement was right on the water, it stands to reason that at this early time period, those same swords found in the colony were undoubtedly carried by those ships on the shore.