Most state departments of transportation have traffic volume or traffic count maps.
These are excellent resources for finding lightly travelled roads.
Of course, these only apply to state highways - not county roads.
(Some states also have county road traffic info, too.)
Shoulders tend to be something only on busier roads.
Really - an empty road needs no shoulder.
But a busy road with no shoulder is something alse altogether.
Some states also have shoulder width info.
Beware state bicycle maps - they vary from fair to awful.
As for traffic counts - AADT - average annual daily traffic is the number.
Under 500 - Ideal
500-1000 - Very Nice
1000-2000 - O.K. but requires more attention
2000-4000 - Really need a shoulder for comfort
4000 plus - Constant traffic - with a shoulder O.K. but hardly idyllic