How odd indeed! Thank you sepoy1857, Carlos, and FifteensAway. It really seems like at some point in time, a Death Head Hussar inspired unit existed in Mexico. Aside from the Hussars of the Guard of the Supreme Powers, the only other properly named hussar unit I could find was the short lived Escuadrón Provincial de Húsares de Oaxaca (Hussar Provincial Squadron of Oaxaca) which was raised around 1820.
I'd to believe that the black hussar on the painting must have belonged to a unit raised during the First Mexican Empire. As Carlos has said, Chile had a black hussar unit fighting against the Spanish royalists. It would seem weird to me that, almost at the same time, the Spanish would raise a black hussar unit to fight against Mexican insurgents.
Nevertheless, I'll heed Fifteens' advice and have them on my tabletop even if I don't know who they are or where they came from. I'll just have fun!