Asking the park ranger about my planned itinerary, her answer was to take, instead, a 4-lane divided highway with wide shoulder, the argument being that it would be safer than using 2-lane/little-or-no-shoulder country roads. Adding that "people drive like crazy" on country roads.
I've heard the same argument offered by a park ranger at another location.
I personally hate riding on highways, because of the noise but also because this is where the occasional narrows (e.g. bridge, overpass) appears to present more hazard potential, and based on the impression that the difference in traffic volume makes it more likely that a DUI/sleepy driver might hit me.
Anyone would be familiar with a source that would offer some indication of the probability of serious or fatal injury suffered by a cyclist as a function of the type of road?
EDIT
As much as I appreciate the sensible opinions expressed below, I couldn't find any evidence to support the impact of road type on hazard.
The closest that I found is a statistics from the UK comparing built-up vs non built-up fatalities and serious injuries for various types of vehicles. The proportion of incidents affecting cyclists vs motor vehicles driver/passengers is the same, irrespective of the road type. Same for A vs B roads.
Another way to look at this question - none of the reviews on the etiology of cycling mentioned the type of road. Mentions were made about the hazard posed by intersections (car attempting a right turn while a cyclist overtakes on the right; failure to obey stop or light) and dooring.
Sorry for not providing links to sources - I am on tour and using a phone to post/edit