Probably. Find another incoming because LGA-JFK at that hour is a complete wild card but unlikely to be much less than an hour in a taxi.

Any delay on the incoming (pssst, they do have some of them at LGA ) and you might as well just turn around and go to a
WN desk to arrange for them to take you home. Arriving at that hour I would not be comfortable with less than thee and a half to four hours to get over for an international flight on a separate ticket.

From what I know, there is no such thing as a ticket to Europe with WN combined on it so you are flying completely without any protection.