Advice about a stray/feral tuxedo girl

Mattingly and Harlie's Mom here... this is probably going to be a long post, so bear with me.

Last April we all moved to a new apartment building. I was relieved at first not to see any ferals around, since there were so many in our last neighborhood (Mattingly was one as a kitten) that it used to break my heart all the time, even though I knew they were being fed by the local rescue group (that we got Harlie from). A few times over the past few months though I noticed a small, black and white cat that I assumed was a female based on her very small stature. When I saw her this past Sunday, I noticed that she was limping and decided I needed to catch her and have her looked at. It was the first time I had noticed the limp, but my husband said he thought she always limped. So I got in touch with some local rescue groups and found a lady who was willing to loan me a Havahart trap and show me how to use it and everything. I was able to get everything Tuesday evening, so I put the trap out then and again on Wednesday (I got permission from our building super to trap the cat on this property). I brought it in at midnight though because the lady who loaned me the trap warned that even though we live in a very populated area, she tends to catch things like raccoons real late at night, and since this trap does not have a back door, it would be very hard to get a raccoon out. So I put the trap out from 6pm to midnight and got nothing.

Late this afternoon, around 5:20pm, I was walking home from the grocery and there she was just grooming herself in the middle of the sidewalk. Since she was grooming her delicate parts I am now almost certain she is a "she", but then, that fur is black so it's hard to tell. Anyway, I had some cat food in my bag, so I popped the top off one and put it on the sidewalk. At first she hid under a car, but I backed far off the food and she came out to eat. I moved it to the grass so she would be out of the way of everything, but even though we were not on a main road, we were still on a pretty high-traffic sidewalk, especially at that time of day. I of course didn't have the trap or anything with me.

I was able to get a decent look at the back leg that she limps on and it's clearly an old injury... almost like she was in a fight or hit by a car. The whole leg is turned out a bit at the hip. She gets around on it, but I worry because she really needs her back legs to be strong to get away and defend herself on the streets. Otherwise, her eyes were clear, there were no visible mites in her ears, and her coat was pretty shiny and rather healthy looking. She ate about half a can of food before she got completely chased off by a young child (I won't go into my frustrations about that). One lady that stopped while she was eating did tell me that she knew about some people who fed strays/ferals a few blocks over, so I felt better knowing that there is some source of food out there... and I was also heartened that she ate only about four feet away from me, so she must have had some experience with human contact.

Anyway, now I don't know what to do. I've never tried to catch a stray/feral before, and the fact that we don't have our own property/lawn/garden makes it very difficult. Where I saw her today (about half a block away from where I was putting the trap) I don't think i can put the trap out. There are no bushes to hide it in, and it was in front of another building, so I don't have permission to trap there. Not only that, it's right by a dog walk where locals take their dogs in the evening to do their business. I don't dare leave the trap in plain sight since it's not mine and I don't know if it will be tampered with or stolen (though obviously I would replace it if something were to happen to it). And I obviously can't sit out with the trap on the sidewalk all night. I'm thinking about going out tomorrow at the same time with food and the trap, but I'm wondering if I should try something less intimidating like putting the food in one of our carriers and trying to close the door with her in it. I just don't know. I've never done anything like this before. I thought about trying to find the people who feed the strays and ferals in the area, but I wouldn't know how. Our block is all large apartment buildings, and the houses a few blocks over are all close together and have high fences, so I wouldn't even be able to see into yards to see where food and shelter is set up. I walk these neighborhoods quite a bit and never noticed anything. So I just don't know the best way to proceed. Prayers and any advice are tremendously appreciated. I'll keep you all posted.

Thanks,
Harlie and Mattingly's Mom