I'd think the easiest thing to do would be to depart to the south-southwest and ask for an early frequency change. Call up EWR on 127.85 and ask to join the Newark Route east, overhead, then Hudson River northbound with flight following to OXC. Have a copy of the NYC Heli Chart handy. It can be very helpful in getting around the NYC Class B at low altitudes, when straying from the Hudson River.
Doubt you can request flight following from clearance delivery at CDW. Some Class D's provide it, others don't. I was once told that only Class D airports that provide "Stage 6 Services" would give FF from the ground, but not sure how Stage 6 is determined or what the other stages are.
Newark's pretty friendly to deal with and this is a straightforward request. They'll probably tell you to join the Newark Route eastbound, maintain 1000', fly over Runway 4 or 22 numbers depending on what's in use, then join Hudson north. Around Chelsea Piers, EWR will hand you off to LGA, who will hand you off to NY Approach somewhere between the GWB and Alpine Tower, and they'll take care of you from there.
Can't help you for IFR, but as Jason says, Skyline is VFR.