What is a shaker hood exactly?
It is a passive forced induction hood, meaning it works when the car is moving.
There are other styles of hoods that offer a passive induction, such as a cowl induction hood and the reverse teardrop (not as good as cowl induction).
Yes, you could use other systems, see if you can find a parts man at Ford to look up the part numbers for the extra intake systems for the police version, or find a wrecked police car in the salvage yard and get the cool ram air system off of it. It might not be as impressive to look at, but it will work better then most aftermarket set-ups.