Dan,
Instead of finding a different sport maybe find a different gun.  Revolvers aren't dry fired after the "unload and show clear".  Revolver shooters are just told to close the cylinder and holster.

OK, gotta shoot a bottom feeder?  You gotta dry fire.  It's a standard and essential safety procedure for everyone.  Give it a good try at a couple of matches and the phobia against dry firing will be greatly reduced.

Scott