To be honest, I'm not sure I understand the concern a police officer might have with an exposed knife. It's not like you need to hide anything, if you're already walking around with a gun, baton/nightstick, 3D cell Maglight, pepper spray (perhaps), etc. The only situation I can think of where a visible knife might come into question would be when cuffing or subduing a suspect, he sees the knife and makes a grab for it. If this is a problem/concern, you could always carry the knife in a fold-over sheath on your belt.
If you're still concerned about a knife being a weapon, there's alternatives. There are several companies that make rescue knives that are specifically designed for what a cop should be carrying a knife for. Check out the
Spyderco Assist. The tip of the blade is completely blunt so it's useless as a stabbing weapon, and nearly usesless as a slasher. But cutting seatbelts and flexi-cuffs is easy with minimal risk to whomever you're freeing. Squeeze the blade when the knife is closed, and a carbide glass breaker pops out. With this knife, you can break a car's side window, cut the seatbelt, and rescue a person from a car, all with one tool. The knife even has a built-in whistle. If you want a really specific tool, look at the
Benchmade Rescue Hook.
I said in my first post that I'd reccomend to all cops to carry a knife, but let me now extend this to multitools. A knife with easy access could prove to be invaluable, as could a multitool with a good pair of pliars and various screwdrivers. A great comprimise would be a Leatherman Ti or XTi, which combines the multitool with an easily-opened blade and a pocket clip.
I see much less need for concern about how well a cop's knife would perform as a self-defense tool. A cop will have much more effective tools at his disposal (gun, baton, big flashlight, etc), and more importantly, his training, to keep him alive. I'd expect a knife to be the very, very last resort.
I see lots of cops here that carry a knife, and often I'm pleasantly supprised to see a real quality knife. Spotted a Benchmade auto in a cop's pocket just the other day at Whataburger (probably a 9050 or 9100). Still more carry a multitool of some sort on their belt (usually Gerber or Leatherman).
What I'll expect you'll notice, if you start carrying a knife, is that suddenly you'll wonder how you got by without one. Most people simply don't realize how useful a sharp piece of metal can be in urban daily life. I use a knife all the time at work for opening boxes and food packaging. I use it at home to open mail/packages, to get the plastic wrappers and those infuriating "Security Device Enclosed" stickers off. I use it at Circle K to cut those plastic tie thingies they bundle newspapers with when the clerk forgot to. And I dare anybody to open a clamshell package without a very sharp tool (or a welding torch). I gave my old Leatherman Squirt S4 (small keychain tool with scissors) to a friend, and she's amazed at how useful having a dinky pair of scissors is. My point is, even if you buy a knife to carry for only for those rarified situations where a knife can save somebody's life (including your own), you're going to find that you use it much, much more than that. You'll wonder how you ever got along with out it. And if you forget to carry it one day, I'll bet that you'll come across a situation (no matter how minor) where you wish you hadn't forgotten it. That's the main reason we here carry a knife (or several). It's simply a damn useful thing to have.