I’d go with the live trap and friendly notice to the owner.
I caught my neighbor’s cat a few weeks back and they were just happy that I use a live trap and said they’ll try to keep him in at night. I don’t have any issues with the cat but I tild them that I trap coons and possums so if their cat didn’t come home they could check the trap.
Two years ago I caught a neighbor's cat. the first time I let it go and the second time I put in a pet carrier then walked down to her house to tell her I had it. She had been warned numerous times by the condo association but she firmly believed that just because she let her cats onto her front porch, they weren't going anywhere.
Well, I made her come down to pick it up and I never saw the cat again. What really pissed me off was the fact that this was a really friendly cat walking around in a subdivision with loads of traffic.........