Paul,
welcome to the forum, in the US, Stage III would almost always include adjunctive chemo and radiation, especially with a nodal involvment. If it were me, I am not so sure that I would want to "escape" radiation and chemo. Recurrences can be very unforgiving.
Here is a link to the NCCN oncology practice guidelines which are pretty much the US standards of care.
http://www.nccn.org/professionals/physician_gls/PDF/head-and-neck.pdf Definitely a choice you have to make and very carefully consider. I would get second opinions.
If you do choose radiation you should be recovered enough to still make your cruise.