I have several cats and have never had them get into my quail pen and it is outside. I think you are safe.
I bought some feeders for birds at wal-mart that had (oh it is hard to explain).. a screw on cylinder to a feeding end, it wasn't made to attach to the outside but I used a peice of wire and did it and it worked great. I cut a hole for the feeding end and wired the cylinder to the outside(it may have been a guinea pig feeder or something like that). Anyway, now that I have quail again, I need to get some more. If I do, I will post a picture of them. They hold about twice as much as your feeders do.