Fellas: I don't think it is the hammer/sear that 'clicks' when you bring the hammer to full cock, I think it is the cylinder lock that seats, and clicks, when the cylinder is fully indexed. I've tried a number of different ways to cock the hammer back on my revolvers without making any noise but it seems that no matter how I work the hammer or trigger, what makes it 'click' is the cylinder lock - or whatever ya'll call that little gizzy at the bottom of the cylinder well that locks the cylinder into position for firing.
I think the only way you can get away from that noise without spooking your intended game is to learn to shoot accurately using double action only. That way, the 'click' you hear is drowned out by the muzzle blast and your intended target doesn't hear that part of the action working. But, as some of the other fellas said, that noise is minimal and does not often alert the animal to your presence. Something like a shotgun shell being chambered sure does, but not so much the click of a double/single action revolver. Hope this helps. Mikey.