As we all know the majority of players don't bother taking any ship that isn't the rustbucket into raids and the only reason to use a non rustbucket ship is if you are planning on picking up salvage and fighting other ships. I think there are a number of reasons for this but for me the main one (as a mostly solo player) is that it is insanely easy to lose the ship whilst all it is doing for me is sitting in the hangar. There are other problems besides how easy it is to lose but, well, I can't fix everything!
I think to help with the above any (non rust bucket) ships that you own would remain assigned to you until the raid is over and unless an enemy actually takes the ship it is returned to you. I think that it should remain in your hangar but show as "unavailable" so that you can't "overfill" your hangar but that unless it is ACTUALLY taken you get it back. This would also allow you to pod out of raids as the ship owner without that being a massive loss.