Im not the most experienced or well-versed source but I have a bit of a leg to stand on as I've been researching this stuff pretty extensively recently. I just turned 18 and i plan on going on a long solo tour this summer as well. What Ive learned is that its much safer than most people think. All the journals and discussions Ive read by those who have done this before say that the most dangerous part of this trip is not the people you'll see but the cars on the road. Not all bike routes are perfectly made or completely up-to-date so even some traditional bike routes have some thin shoulders you'll have to work through. As far as strangers go, Ive heard almost exclusively great things about the kindness of the strangers along the route. With the exception of a few pissy drivers, Ive only ever heard of one instance of a stranger being a creepo.
Then again, all of the people I've spoken to have been guys. I imagine its slightly more dangerous to do this trip as a young woman because it does seem to make you more susceptible to confrontation by the occasional creep.
Personally, my mom has been freaking out about my safety too. My dad suggests i bring along a pocket knife or some mace just to give them and i some more peace of mind. I think that might be a pretty good idea for you too.
Anyways, i hope your trip goes well! Good luck!
p.s. i just realized how long ago your post was from...hope I'm not too late with this one