I gave you the tidal/current information for the days you asked about. I avoided, giving the do-it, don't do it type of advice, since you didn't ask for that.
However, now that I've read your post again, and the other comments. I would add that I would not want to make this trip in 22 catalina that I've just purchased and haven't shaken out yet. If, in fact, this is a new boat to you?
I'd want to have confidence in that engine.
I would also probably have, at least my mainsail up..and the jib hanked on, secured and ready to go...just in case that baby quit on me.
I would also want an excellent Weather window. Fuel will be an issue, and I don't think City Island is a good fuel stop, I know I can't get diesel there.
So, for a re-fueling stop, you might have to stop in Manhasset Bay. The Capri Marina is the 1st stop inside there, I believe to port. I've re-fueled there once.
I sailed a Catalina 22 for a number of years on Barnaget Bay...it's a great little boat, but..for the East River, New York Harbor, The Narrows, Etc...and the Ocean, you really want to pick your day! And hit your tides and currents. An early morning Weekend day, would be best..(If the weather was right.) The ferry traffic during the week is pretty hectic, and it gets choppy in lower manahattan....The Narrows can be a nightmare, in the wrong conditions in a small boat. ( wind against tide)
In great weather, it could be a great trip...Just know what you're up against if the weather is iffy.