I hate to suggest it but your fastest most direct route would be to sail it. You are in a coastal community so sailing at a good clip would put you in your destination faster than sitting through rush hour traffic or spending the time getting to the train station, etc.
You can find a good quality sailboat for about $5000 at the very cheapest and you could get lessons for about $300 on how to sail (although the basic principles are quite easy).
I would recommend that method as probably your best bet in terms of fastest most direct route. It would likely take you an hour by sailboat with good wind and minimal outboard use to get there. Just make sure you are comfortable with open water ocean sailing as you would be covering a very small stretch of open water in between both cities in the Atlantic Ocean.
I assume that once you’re actually on Manhattan, all commute problems have the same solution: Subway if you’re not in much of a rush (in this case, probably Wall St station, take the 4 or 5 train north), or cab/Uber if you are.
Just curious, but what do you do once you get to your destination? Is there a secure place to park your sailboat? What does it cost? Can anyone just sail up anytime and park there?
Can you sail in bad weather? What about in winter?
There are 2 marinas with slips in Manhattan, you would need to contact them for a slip rate however (Find A Park : NYC Parks)
Typically you can pay for months in advance and it generally is done according to the size of your boat (length).
You can definitely sail in any kind of weather, winter included. Its the ocean and the ocean is not going to freeze over and I’m not sure when the last time was that the Hudson froze all the way over, I’d have to look into that. Either way sailing would work as a multi-purpose year round way to get to work. Sailing in bad weather would be challenging but if you wore appropriate rain gear and waders you could prevent even the nicest of suits from getting wet or soiled.