Careful, those currents are mighty tricky, both off the Battery and up above Inwood. Probably too tricky for swimming. You hear it all the time when bodies and other things are dumped in the river-- they wind up in odd places like Hellgate or Little Brothers Island.
I have my eye, however, on those kyacks bobbing away below N. Moore Street. Anyone want to join me?
There's also the old freight railroad trestle at the point where the Harlem and Hudson meet. You can enter through Inwood Park in the Northwest corner of the island and make it across very quickly to the mainland--we used to do it all the time as kids. It's kind of obscure and might not be as guarded or blocked as the road bridges in a time of shutdown.