ok, heres some cons to some of your ideas...trust me i have gone through many...
Trapping
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its a good idea, but releasing it elsewhere, is making it someone elses problem. not to mention that many cats WILL find thier way home.
you also run the risk of catching undesirable animals IE..skunks! you really dont want to have to open an animal trap with an angry skunk that feels pinned up against the cage! squirrels, racoons, and other friendly neighborhood cats that are just outside taking thier noon stroll, then get put in the house for the rest of the day are unwanted as well.
Shooting
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Great idea, but again the problem isnt solved. there are still these cats in the neighbors yard, and will piss, sh!t and mark your front yard up when youre not around with the gun. i say if youre gonna shoot the bastards, kill them dead. pellets to the head arent good enough either, they will probably be lingering for a few minutes, crying which is unwanted due to the draw of attention. you dont want your neighbors complaining that thier kids had to see that by accident.
Moth Balls
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Works sometimes, but not all the time.
my solution....
i say find a trash barrel thats big enough to fit the entire trap into it. i mean completly inside the barrel. fill the barrel with water, and drown the f!ckers. put em in a few trash bags and dump them at the local dump. no contact with the cat, no noise and its clean. no blood or torturous pain from a miss fire that hit its shoulder instead of its head. a sure shot way of getting rid of these guys.
good luck
not2sure