Hi Clint,
One of the first symptoms of radiation, at least for me, was the reddening and burning of my skin on the outside. By the end of my six weeks of treatment, my skin in the radiated area was much too tender, blistered and oozing to even think of shaving.

Like you though, the parts of my fact that weren't getting radiation bothered me because I couldn't shave with a safety razor. I ended up getting an electric razor for this period to shave the areas that weren't radiated every couple/three days, just to try to feel somewhat normal.

By the way, my radiated areas no longer have any hair growing, so I only have to shave parts of my face. The downside is that if I decide to skip shaving for a day or two, it looks like I started to shave (the radiated areas) and then somehow forgot to finish. I don't want to give people more reason to think I'm getting senile, so I usually shave daily now.

Hope this helps. Good luck with your radiation treatments. - Sheldon