Even though you have a Will, and you plan on leaving everything to one person and that person also will be the executor, it may make sense to consider what assets you may own that are NOT held in your own name that might be payable on your death. For example, life insurance benefits are paid to the beneficiary named in the policy or on file with the life insurer and not to your estate (unless no beneficiary is named or the one named pre-deceased you). Savings accounts held in a Totten Trust or where a beneficiary is named also get paid to the person named, not the estate.
Have you considered what might happen if the person you named as your sole beneficiary in the Will were to predecease you? Have you named alternate beneficiaries? Have you considered using a Living Trust to hold your assets so that there would not even be a need to file probate in New York -- as even with small estates going through probate can be a hassle and undue expense for the beneficiary, which diminishes the amount he or she ultimately receives, and will delay and complicate receipt of the assets you intend to pass along, especially if any of your family members who would be heirs at law file an objection.