I am into chickens long-term have interest in wildlife as well. Going after a single predator I did in the beginning although found had no real effect on controlling losses when you consider the number of birds I have and how they are spread out over the landscape, even at night. The approach...
You do it to be smart. No birds to risk and you know you have current predator pressure. Put the trap in the coop / pen. Bait with chicken or feed you think predator is looking for. If predator can not get in then upgrade is sufficient. If predator challenging setup not present then you...
Trapping for me allows for confirmation of predator ID. With no birds, I would even release caught animal to enable testing of coop upgrades since no chickens would be a risk. Creating trapwise will not be a consequence once upgrade complete.