In general, the airspace below a Class B shelf is Class E airspace until 1200' or (more often) 700' AGL, and then Class G to the surface.
Immediately surrounding the Hudson and East Rivers in New York City is the EWR/JFK/LGA Class B airspace, which has a floor of 1500 MSL in that area. Over the Hudson River the floor drops to 1300 MSL; over the East River the floor remains 1500 MSL, except within the LGA surface area where the floor is 1100 MSL.
Over the two rivers and below the Bravo floors are the Hudson and East River Class B Airspace Exclusion Special Flight Rules Areas, which are defined at 14 CFR 93 subpart W.
This is excluded airspace is, of course, not Class B, because it is explicitly excluded from Class B airspace. Is it Class E and/or G airspace, as expected for other airspaces below the Bravo shelf? Or is it a "special" non-Class E/G airspace area?
Practically, what are the visibility and cloud clearance requirements in this SFRA airspace?