You can use ardupilot for gps free navigation, but then you need to send your position estimates to the flight controller. I.e. Ardupilot needs to know your position, even if you calculate it on the companion computer and wanted to send motion commands that account for the known position. Without knowing your use case, I guess the feasible approach is to leverage the Ardupilot features(eg. position controller, velocity controller) instead of disabling them and then Ardupilot needs your position estimate. If you want to make your own high level contollers and send attitude targets then you can have a look at GUIDED_NoGPS.
I have not found a general description of how to do send the position data you calculate to Ardupilot, but the docs contain some examples(ex1, ex2) where they send updates with the VISION_POSITION_ESTIMATE mavlink message. There is also some blog posts on this forum addressing this issue(ex1, ex2).
I have not tried any of these myself, but it would make a very cool project.