While I can't speak for the 19th century, I've written before on earlier Asian contacts with colonial Mexico - with a focus on the Aztecs - that you may find interesting:

• on the two Japanese missions to Mexico

• more directly on Aztec warriors in the Philippines

• on fillipinos and one samurai in Mexico

While these don't directly answer your question about exact knowledge (difficult for the 17th c.) they do show traces of early modern exchanges between Asia and Mexico - including cases of native Americans working on the Philippines and of an Aztec scholar describing a Japanese delegation.

Hope this helps!