Sophie,
As you can see by my signature, I had the same staging as you, but I DID have the neck dissection. Although my neck CT scan was clear, it was my surgeon's protocol to recommend the neck dissection. There is no standard for the recommendation of neck dissections, however his particular feelings were that he could only tell for sure that the nodes were clear by removing them.
I hope this doesn't confuse the issue for you, but will give you some additional information to possibly help you make a decision.
Because the lungs can be a site for metastasis, I do get a chest x-ray once a year.
Jerry