I believe if you google up minnow seine and dip nets most of the ones I am seeing are of the squared/rectangular variety. The important thing to notice is that they are legal in Lake Erie and the harbors so there is no reason why a cast net would not be otherwise they would be called out in the regulations.

Actually after posting all of that I started looking up shiners and Lake Erie on YouTube and there was a lot of good video's out there on catching shiners, some in area that I recognize as well. Seems most people are using Umbrella/Dip nets to get them. I will probably end up ordering one of those to try and catch and freeze a bunch in the spring for later in the year, I know in April they are so thick you could walk on water in the marina around the harbors.