Of course there is 95% of chances that these short swords are US in origin.
But remember that the US artillery sword is based on the French model.
This model existed since the 18th c. and Lafayette with the models 1767-1771 and 1774-1783.
I'm not in the head of a 19th c. Indian, but a sword with an eagle head is a really cool totem... Think about it....
So you need to look at the photos closer, maybe these Indians had French swords.