My mother's mother is Belgian, specifically Walloon. My mother's father is from somewhere in/around Russia and we've always found it easier to gloss that as "Russian" as they went to the Russian Orthodox Church. My father's mother is the one who did the paperwork to join the DAR.

With that said, the first Europeans in NY were not, as you've been told, the Dutch. They were the Walloons. The Dutch came a short time later. Peter Minuit, in fact, was also Walloon.