This instructable is more about what Sugru, a clay-like silicone rubber product, doesn't stick to than what it does stick to. The mouthpiece has an inside air channel that conducts the air you blow so that it hits the leading edge of a wedge. The sound vibration is generated there. It's the same as a recorder mouthpiece.
Unlike a recorder, which has fingering holes, a slide whistle has a sliding plug inside the body of the whistle. By sliding the plug back and forth, the air chamber inside the body is modified. Deeper notes are achieved by sliding the plug toward the far end of the instrument, creating a larger internal air chamber. Higher notes are made by sliding it up near the mouthpiece.
At the end of the instructable is a sample tune improvised with the slide whistle.
Step 1: Making the Mouthpiece
If you can't find this material, you can probably use something else of about credit card thickness and make it non-stick by first coating it with some dish washing detergent and letting it dry. Detergent is the same mold release agent that I used in making the Sugru sliding plug for the whistle inside a section of pipe. More on that later.
I stacked the strips in such a way that they represented the air space inside the mouthpiece, and strapped them all together with a little cellophane tape.
After heating the end of a piece of 1/2 inch CPVC pipe to soften it (like PVC, only for hot water use), I inserted the stack of strips and squashed the heated CPVC down over them to hold them. I heated the CPVC with a propane torch. Be careful not to burn it, as the frumes are toxic. I used a longer piece of CPVC, which made it easier to work with, and then cut the pipe to length
After about 24 hours, the Sugru hardens up and the plastic strips can be pulled out from whichever end is most convenient. Start with strips at the center of the stack, since they have less contact with the Sugru and tape. I used narrow pliers to pull them out with.
To make the perfect whistle, I would have preferred to make many mouthpieces, each a little different, modifying the internal air channel shape (width of the plastic strips used to form it), and the angle of the wedge that creates the sound. It takes a good deal of air to blow this instrument. Smaller air channels would use less air, but would would probably create less sound volume, also. The finished instrument could be better, I'm sure, but at least it works.