my cats will catch big black birds (and bring them inside ALIVE!!!!) so I wouldnt put it passed mine to take a young chick for a little spice to the lizards and mice of usual. My chicks are all decent sized 9 week old silkies and adult silkies and they just sit out and watch them now that I let them free range. However I would never trust my cats around chicks under 5 weeks, I could imagine my cats bringing them to the door with a sassy growl going "MINE"...
Since they're in a coop, do like I've done and my neighbor does when he's rearing chicks 4-10 weeks in summer in a rabbit hutch like pen...Put down lime, then in a day or two rake or shovel the first couple inches out from under there and dispose of it, then add sand down under it with another healthy handful or two of lime mixed in. This will keep it from getting grossly muddy, reduce smell, but you will always need to scoop or rake it up because poop is poop is poop and it will stink if its left sitting around in the rain and heat!
Good luck though!
Neighbors being peeved at you for the chickens? Why? Its they're cats that are coming in YOUR yard not your chickens coming in THEIRS. Point this out to them that you're restraining your chickens to your yard, and they can't control their cats, so whos got the animal issue? Is your yard open access between you and neighbors or do you have a fence? Fence - add a string or two of electric fencing by it or just around the area of the coop and have a real low voltage, cats, dogs, whatever will learn awful quickly it isn't worth the ouch to check out the chicks and wander your yard. Neighbors complain about that, I'd tell 'em 'oh well' I've had too many issues with neighbors and their animals being let loose and not being restrained, sorry but my cats stay in my yard and my dogs do too - I make sure of it.
My chickens free range all day, and the other neighbor has chickens, ducks, guineas, pigs, goats, hunting dogs, etc etc and so obviously we get along great
we share ducks and the ducks and chickens all run back and forth across our two properties its too funny. But where I used to live I lived on a dead end road with 5 other people and 4 of them had dogs they didn't restrain AT ALL. And they wanted to gripe the one or two times one of mine got loose and went hog wild X_x some people are just screwy though.
Anyway, take care, and good luck!