Every state has different laws and procedures for how to contest a traffic infraction or, in some cases, misdemeanor traffic offense. It doesn't hurt to contact a Delaware attorney to have a better understanding of your options. While you might not be able to make the trip from NY, sometimes an attorney can appear on your behalf. Also, while you might not be able to afford legal fees, you might also not be able to afford increased insurance premiums and having this on your driving record. It's important to weigh everything.
This answer is given merely for informational purposes and does not create an attorney-client relationship. For specific advice, contact an attorney in your state to see if working together makes sense.