It's a surname and surnames are always unisex to me (as they are used by men and women, except for names that also have a history as a first name such as
Hannah or
James). So I find
Schuyler acceptable on a girl and know a female
Schuyler.
I do however think that it's also very handsome on a boy. Yes, I thought that some people would say shoo-ler. Your son has a great name!