It is tough to not be scared before surgery...especially after the experiences you have already had. It sounds like your surgeon is being methodical in his work up. Imaging and FNA can better characterize the lesion. Pathology slides can be reviewed at different institutions if a second opinion on the biopsy is being considered. Having two surgeons working together during a procedure is not uncommon. Obviously, there are many important structures within the neck. Your surgeon is trained to protect them. The risks for injury to the nerves and vessels are low, but they are real and that is why he discussed them with you. If you are concerned about having the procedure, you can always get a second opinion. That way another set of eyes can review your history, physical, imaging, and pathology. No recommendation is appropriate unless all of these pieces are examined. If you have a good relationship with your ent, you should definitely discuss your fears and concerns. Best wishes.
How long have you had the mass? Did it come on suddenly or gradually?