Wrist braces do help some people by steadying the slingshot or supporting a weaker wrist. However, I find it much more accurate and comfortable to shoot without a brace. The deal is in how you hold the slingshot. Without a wrist brace you don't want your index finger and thumb down on the grip like you're griping a hammer. You want them both up on the forks. The index finger wrapped around one side of the fork and the thumb pressing forwards on the other side. In this manner you are steadying the forks while keeping things low in your hand to greatly lessen the torque. With the hammer grip the forks are sticking up really high and the pull of the bands exerts a lot of torque on your wrist. Plus, a non-wristbrace slingshot is much much much smaller and pocketable than a wristbraced one.

Hold like this: http://www.dankung.com/dk/images/XIE.JPG