They will, and it might be smart enough to avoid a trap. Here's some things that we have done, when we have predator problems.
Get a radio if you can run it on an extension cord or something so it's right in the chicken house. Put it on a timer, or better still just go out there and turn it on and off at random times throughout the day. Try to make it the same volume as a human voice talking to another human, or a little louder. Turn it to a talk radio station. I find that it helps if I keep changing the times of day that it's on and off. And move the radio around to different locations, too.
Game camera s a great idea if you can get one.
When we had the problem with the foxes last summer, I would go out to visit the chickens same way, at random times throughout the day, and never at the same time.
I always talked a lot and made a lot of noise when I was out there. I also drove our Gator out there sometimes, or the car, tapping the horn, blaring the car radio. Sometimes I I took pan lids out there, and would walk around smashing them, and flashing them in the sun. Now, I work out of the house, so it was easier for me to do that, but I do think it helped, although it was time consuming.
We also have a "bird banger" or "bird bomb" gun. WE had to get a permit to have it. It's for scaring away problem birds, but it works well for all predators, just don't use it too often, only if you're pretty sure there's really one around. It doesn't hurt the predator but it does help to scare them off. Failing that, you could try just ordinary Black Cat fireworks, or bottle rockets. Or anything you have that makes a loud explosive noise and has that gunpowder smell. Just randomly shoot some of those off once in a while, whenever you think the predator might be around.
And lastly, there's a thing that I want to get, although it's about 180.00, it's free shipping. It's a solar powered, motion detector activated sprinkler, that also makes noise. It would be hard to use in certain situations because the chickens would set it off, but I'm thinking of getting one for our garden this summer, or even just to set outside the barn at night. It stores the solar energy so it will still work after dark. You could set it outside the chicken run or house, and it might work.
What are you using for bait in the live traps? Glad you let the baby skunk go.
Do you have a dog? Maybe try some Guineas? Get those geese over there!