RE: NEVER USED A PEEP WITHOUT BUNGEE
Now I am just the opposite, I have never ever used one with a cord and never will. I have been using the Fletcher Tru peep ( the Super Hunter) for years now without a tube. I was always afraid of it getting caught on something while stalking, or when you are pulling the bow up in the tree etc. But my biggest all time fear was to drawing back on the trophy of a lifetime and the cord popping off or breaking.
With the great strings that are being offered today to eliminate it twisting, you should be just fine without the tubing.