Why not set and bait outside rather than encourage them to come inside the run? handling a trap every night is self defeating and your scent is on it heavy. A secure coop with a good latch will keep about everything out short of bears.
What is the situation? what part of the country are you? what predators are you fighting? What's your coop & run set up?
I have seen bout everything here and the coons play on my porch (i swear to tease the dogs) so far nothing has bothered my chickens but ots been only a few months. Outside the run would most likely catch cats only. They stare at my birds all day. We have rats in the barn. Possums coons foxes skunks coyotes are all around. Thinking just extra if they got in (no bait just the trap laying in front of the door to hopefully catch anything that did get in)
The thing is, they usually don't just come strolling in through the door. They dig in, tear their way in or climb in. I agree that you're better off just beefing up your coop. Good, heavy wire around the outsides, a sturdy cover on top, make sure there are no gaps, either put an apron of hardware cloth on the ground around the bottom of your coop or dig it down 18"-24" for the burrowers. People also put electric fencing around the outside of their coops.
Not the run front door the coop door. Its right now the weakest point. Dh wont approve much more spending and i still have a day tractor to throw together. I cant do electric and have fence buried but a big dog or coyote might be able to tear into the run. Im going to get a padlock soon for the coop door and recut for a better fit. Just happen to find an old leg trap sitting in my shed. Otherwise only a bear is getting into my coop its only windows are locked up high and have wire to keep chickens in and predators out.