You would only be in Delaware for less than 20 miles going through Jersey. But why deal with NYC? Southern Jersey isn't bad, except you have to go through NYC, Philly, or Wilmington to get there.
As long as you are properly licensed for your home state, another state can't write you a ticket for not having the proper license. That's why NJ can't write a ticket for not having a rear plate on a semi tractor if you are from PA, where a front plate is the only one required.