I've taken both folders and dive knives to Cozumel several times with no problems. Can't tell you what the law actually is, but I've never had any problems at the airport (where they WILL go through your bags most times - coming and going) and I've seen people walking around town wearing dive knives with no problem. (Looks silly though.)
Can't imagine a scenario where you'd be stopped and searched. I've seen people totally drunk and out of control and the cops just looked the other way. Just be polite, respectful of the churches and local people, and obey traffic laws if you rent a moped or car. A lot of people speak English there now - if you have a question about something just ask. Friendly, mostly honest people (don't leave gear unattended on the beach, though.)
The airport officials are used to tourists bringing in all kinds of expensive gear. The only definite Don'ts are pornography, stuff you clearly intend to sell (friend of mine brought 5 Seiko dive watches) and drugs. God help anyone caught with drugs.
Check out the 3 and 1/2 club in Cozumel, and make a day trip to Isla Mujeres if you have time.