There is a sign saying no guns (In Ohio, that sign carry's the weight of the law if Im not mistaken), but no metal detector's, or pat downs.
We've never been, but the map shows it on the Kentucky side of the river. What's KY policy on signs? Similar to IN iirc.
Frank_N_Stein is correct, although I think the bag search may vary depending on the day. Last time I went was during the week and I don't remember any bag search happening.
The aquarium is in Kentucky, so the signs do not carry the force of law. Keep it concealed and on-body and you won't have a problem.