I'd say second cousin, and born after the Finding of the Eldar.
We know from PoME that Cirdan was originally named
Nowe. In NoME, we learn in the latest Time & Aging texts XIII.1 & XVII.3 that Ingwe, Finwe, and Elwe were born between the Finding and the March.
Their generation (generations - technically Ingwe is a generation above, though roughly the same age) are the only ones confirmed to have -we names, excluding Finwe's reuse of his own name. Tolkien provides a family tree for Ingwe: Ilion - Ingwe - Ingwil.
It is *wild* speculation to say that after the Finding, -we names came into fashion around Cuivienen, but I'm doing it anyway.
How close a cousin? Your WJ quite slightly implies Cirdan is "remoter kin" of Elwe, but that's by comparison with his brothers and their descendents. We know the grandchildren of Finwe considered each other close kin (first cousins); we know Elrond and Celebrian weren't seen as kin, despite sharing great-great grandparents through Elwe and Elmo (third cousins); so would sharing great- grandparents make you distant kin?
It's the most tenuous chain of logic, but I like it. Cirdan Nowe is Elu Thingol's second cousin.
hS