In such cases, spanking implements that have a great stinging effect while making little noise, such as a cane, may be preferred to those which make a louder sound. Hand-spanking, unfortunately, is probably the loudest of all spanking techniques.
List of common implements, by noise level:
Of course, this is relative to the amount of force used. A single-tail whip, for example, is probably the loudest implement of all, with a crack that sounds like a pistol shot. A hard caning can also be extremely loud.
To quieten down a noisy spankee, having them bite down on a piece of fabric, such as a pillow, blanket, cushion, towel, etc. may be helpful. This is generally safer than using a gag which can cause problems such as obstructing breathing if the spankee's nose becomes blocked. A gag also prevents verbal communication (e.g. using a safeword).