Just to chime in. Ohio as a state has one set of laws, but each municipality can have their own. For example, Akron and Cuyahoga Falls have made 2.5" illegal in a folder. It's on the books. And a friend of mine spent $2500 to get out of a felony charge because he had a thumb opener...like a little Gerber with a thumb button. Is that illegal? Probably not, but it's going to cost you a ton of money to prove that the poorly schooled cop was wrong when he arrested you. That's the bottom line and that's the way it works. Lawyer fees can be their own prison.
Me? I won't carry a fixed knife unless I've got a good reason to...like going fishing or camping. And I'm talking about a Mini-Canadian. Likewise, my wife's got a Pro-Scalpel that she won't carry unless we're camping.
My mother in law was trained by an ex-cop for her CCW (you go, Mom!) and he said fixed blades were a no-no.
The problem is that Ohio's state laws are vague and that they don't override local laws.
Good luck!
(not a lawyer, etc etc)