If you feel you must use a net, choose a soft mesh material rather than a hard, abrasive nylon. Do not attempt to remove a swallowed or deeply set hook. Simply cut the line as close as possible. Fish have a far greater chance of recovering from a swallowed hook than a wounded organ. Hooks in the lip, jaw or cheek areas cause little damage.
Baited hooks are more likely to result in a gill or stomach hooking than artificial lures.
Consider using single hooks or barbless hooks, since this will make releasing the fish much easier. When released, even the most fit fish may need a little resuscitation before resuming its natural behavior. If the fish needs a little nurturing, move it back and forth in the current to get water flowing over the gills. Most fish recover in a minute or so and readily swim away. It might not be up to the challenge of fighting fast flowing water.