Correct, they don't have sweepers.
Wow, this is a close one. It can be either I think, just my opinion. The OP would have actually had to be there before this process begin to know which is true. Why? When zoas typically expel waste, ( great link BTW 650 ) it isn't always as uniform as it is in this picture. Note how even and smooth the string lines are. Poop is usually sputtered out but it can be smoother, I know some are cracking up at that LOL. They can also expel waste and then retract it, I've seen it a few times. It sure looks like poop, but it could be a worm also, not sure. I think the OP will have to decide. Either way, it I nothing to worry about and there's nothing you can do about it. I've even seen polyps do such crazy things as try to consume their own skirts. Again, it's nothing to worry about.
Mucho Reef