Fish that are to be returned should be handled with wet hands for as little time as possible and returned to the water for recovery. With larger fish one should avoid lifting the fish as this can damage the internal organs. If you are not intending to return the fish then it doesn't matter how you handle it as you are going to kill the thing so it can fill up that space at the back of the freezer for the next three years. If you do kill fish, do it so as not to upset or incense non fishing onlookers. We are all ambassadors for the sport.
Courtesy of Carland...
Fish breath via gills using the dissolved oxygen in the water to exchange
the CO2 that builds up in their blood. During the fight, the fish produces
more carbon dioxide, as it's normal level of exercise has increased. Once
the fish has landed the oxygen content in the air is greatly increased in
comparison to the water that the fish usually breathes in. This initially
gives the fish an extra rich source of oxygen that can help in reducing the
dissolved carbon dioxide in it's blood. However, this enriched oxygen
environment very soon becomes poisonous for the fish just as humans would die if
they were to breath air with a high oxygen content, which is opposite to the usual
theory that fish 'drown' (lack of oxygen) if they are kept out of water. They
in fact suffer from oxygen poisoning due to the over rich oxygen environment
that air provides. Once the gills dry out, the oxygen transfer becomes very
inefficient and the fish then drowns (if it is not already dead).
Courtesy of Carl