I may be moving to a clicker to help a bit with TP. I know there are people that use them for hunting. Whay do you do to deaden the click.
I don't worry about the click. Haven't had an animal jump from it yet. If you are really worried about it you can put some mole skin on the blade to quiet it down. I also take the chain off and replace with release rope.
do a search on the Shooter's forum. There are several threads there on clicker set up.
I wrapped mine with electrical tape when I used one. I also took the chain off and replaced it with decoy rope.
Velcro or felt tape works great. But making the clicker thinner makes a huge difference.