You're right that you can't really replace a laser with an LED in this sort of use. There's a basic difference between the light from a laser and the light from other sources.
In an ideal laser source, all the light comes out almost in the same direction, to the extent allowed by the wave properties of light. (Real lasers are often fairly close to ideal.) That means that for a beam of width w the angular spread of the beam can be as small as about λ/w radians, where λ is the wavelength. So for a 1mm wide beam of red light, the angular spread can be less than about 0.001 radians. Beams like that are great for your sort of application.
In other sources, including LED's, the light comes out in a variety of directions even if the source is spread out. You can make a collimated beam by putting the source near the focus of a parabolic mirror, but for a given width of beam the angular spread is still much larger than for a laser. You could throw up a lot of the light to improve the collimation or reduce the beam width, but that is less efficient than just starting with a laser.
If the laser happens to be a diode type, it's built around an LED anyway. Rather than using mirrors etc. on the light after it's been emitted in a range of directions, the laser incorporates the mirrors into the source. It uses the quantum mechanical ability of light to trigger the emission of more light like itself to get the emission to be nearly coherent.
We don't know enough about the particular device you're describing to say how to make your own version of it. However, it's basic physics that says you should start with a laser.
(published on 09/19/11)