I was interested in developing a Rail Shooter at one time and considered a few approaches:
1. Cam XYZ Recorder
2. Waypoint
3. Waypoint w/ Pathfinding
With the Cam XYZ Recorder technique you perform a walk-through in the level with First-person camera, recording camera position and angle data every so many frames. You can store the orientation data in a array and replay by simply iterating thru the array to orientate the camera.
With the waypoint system you can create a special editor to place waypoints that point from one to another. In the play loop, you simply point and move your camera towards the `target` waypoint. When the camera reaches the waypoint (collision check) you set a new target for next waypoint - repeat point & move. Since your not concerned with the camera angle this method might suit your needs better.
For a more advanced waypoint set up you could include pathfinding and obstacle avoidance. To go even further you could probably include some type of physics in handling movement.
As simple as it may sound, you may not need anything fancy and just move the camera forward.