I've not been near v4 for almost 5 years and I don't remember much about
Geodesic but I did find this in a search, see this URL,
Surely there is a capability within the Geodesic function to do what your're after. The next picture is a zoom of the Geodesic Menu, it's blurred but most of the options can be made out.
PT PT should give the geodesic path between the circle centres on the support, and PARALLEL or TAP(er) OFFSET will probably give the curves required. All this is from memory, but it should point in the right direction.
For my own interest and amusement I've done this by construction in V5, so that if it had to be done that way, the same method will apply in V4.
Two circles have been normally projected onto the Support and a line that connects their centres ( on the Support ) normally projected to the Support. This Curve is considered to be path of the centre of the tangential curves, which are Parallel curves offset on the Support, by the radius of the original circles, that were directionally projected onto the Support.
In the Thread question, the simple surface is a
Surf1:Curve Curve where R1 = R2 and are on parallel planes, with their centres on a common line, so the required Curves can be considered parts of a Helix.