Hello Andrew,
as Christian rightfully said, if you don't want to use navigational instruments than you'll be flying almost in VFR rules.
Regarding the intersections: Intersections are usually where airways meet. Airways are typically defined by VOR beacons and a specific radial. So, even with the two VOR's you can still make it to an intersection.
Select the VOR frequency of each Airway into each of your instruments and choose the correct course of each one. Then, when the two VOR's are centered, it marks the point where the airways meet and hence your intersection.
Another easy way is to navigate from NDB to NDB. NDB's do not have radials and as such the arrow just points you towards them. Once over an NDB the arrow will change direction 180 degrees at which point you can select the next NDB's frequency, and do this until you reach your destantion.
NDB's have far greater range than VOR's as they are able to follow the curvature of the earth.
If you insist on flying just with compass and chronometer then you'll need a detailed chart like the VFR chart below.
From there, you calculate your route marking correct heading and distances. Then, as you fly you take your speed and calculate how much time it will take you to reach your next turn point.
However, as the headings, distances/times and wind effects tend to alter your route slightly you must note two important things.
A) Make your segments small (no more than 15-25 miles)
B) Make sure you can have visual references to ensure you are were you're supposed to be and compensate for the deviations.
In VFR conditions the short segments are stipulated by the short altitude of htese flight and distance to be covered in an event of a failure. But as failures are rare in FS you just need the short segments for orientation.
Happy flying
