Perhaps this isn't groundbreaking but just wanted to share this...
I've tried a couple different types of whistles- plastic, corian, metal... I do the best making a consistent sound with a metal whistle but hated the feeling of metal on my teeth. I bought some Woodwind Mouthpiece Cushions, cut to shape and placed on my metal whistles where my teeth bite down. I don't think the pads interfere with the sound at all.
Attached is a picture of a whistle with the pads, same pads on the other side as well