Tall Tines Stickflinger. With a BCY X or Fury string and a pair of wool puffs, the only real sound I hear is my arrow impacting the target, and the bit of swish of the string leaving my fingers For me in recent memory, the Stickflinger is just sensational. My Hill Country Bobcat is also extremely quiet shooting. Both of these bows rival my Hill bow in this regard. And both of them are still really really quick bows.
Those two are standouts to me which is why they are in my stable. Other bows I have owned which fall in your category are the Centaur bows, Toelke Pika/Whip HS, Big Jim Thunderchild, Java Man, New Wood Vanguard, Holm-made, Treadway Black Swamp, Hornes/Cleland Stickbows, Caribow, A&H/ Dryad ACS.